\r\n <li class=\"\"><a href=\"/groups\">Groups</a></li>\r\n <li class=\"\"><a href=\"/ratings\">Rating</a></li>\r\n <li class=\"\"><a href=\"/edu/courses\"><span class=\"edu-menu-item\">Edu</span></a></li>\r\n <li class=\"\"><a href=\"/apiHelp\">API</a></li>\r\n <li class=\"\"><a href=\"/calendar\">Calendar</a></li>\r\n <li class=\"\"><a href=\"/help\">Help</a></li>\r\n </ul>\r\n <form method=\"post\" action=\"/search\"><input type='hidden' name='csrf_token' value='95fc715350206393e9f06bc0fd3eabf9'/>\r\n <input class=\"search\" name=\"query\" data-isPlaceholder=\"true\" value=\"\"/>\r\n </form>\r\n <br style=\"clear: both;\"/>\r\n</div>\r\n\r\n </div>\n\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\"input.search\").focus(function () {\n if ($(this).attr(\"data-isPlaceholder\") === \"true\") {\n $(this).val(\"\");\n $(this).removeAttr(\"data-isPlaceholder\");\n }\n });\n });\n </script>\n <br style=\"height: 3em; clear: both;\"/>\n\n <div style=\"position: relative;\">\n <div id=\"sidebar\">\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Pay attention\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\"padding: 0.5em;\">\r\n <div style=\"text-align:center;border-bottom: 1px solid rgb(185, 185, 185);margin:0 -0.5em 0.5em -0.5em;padding: 0 1em 0.5em 1em;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 1, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:55:01</span><br/><a href=\"/contestRegistration/1876\">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 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=''>13:55:01</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='95fc715350206393e9f06bc0fd3eabf9'/>\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 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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/Nickolas\">Nickolas</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Nickolas\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Nickolas\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Nickolas\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Nickolas\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Nickolas\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Nickolas\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Nickolas\" style=\"text-decoration:none;color:black !important;\">Nickolas'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=\"4269\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4255\"> <p>April Fools Day Contest: editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Nickolas\" title=\"Expert Nickolas\" class=\"rated-user user-blue\">Nickolas</a>,\r\n <span class=\"format-humantime\" title=\"Apr/01/2012 21:01\">12 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>Congratulations to <a class=\"rated-user user-orange\" href=\"/profile/KADR\" title=\"Master KADR\">KADR</a> who was the first of two people to solve all 8 problems!</p><h4><a href=\"/contest/171/problem/A\" title=\"April Fools Day Contest\">171A - Mysterious numbers - 1</a></h4><p>The easiest way to make the problem statement unusual is to omit it. This is an extremely convenient approach — you don't have to maintain the statement in two languages or to worry that it might turn out to be ambiguous or too long or too scary. 690 people solved this problem, so evidently we can omit statements even in regular rounds :-)</p><p>As for the problem itself, it required to sum the first number and the reverse of the second number.</p><h4><a href=\"/contest/171/problem/B\" title=\"April Fools Day Contest\">171B - Star</a></h4><p>They say it's better to see once than to hear ten times or to read a hundred times. In this problem we decided to check this and to replace the traditional textual statement with a single image. Same as in the previous problem, it did well — at least 645 participants recognized star numbers (sequence <a href=\"http://oeis.org/A003154\">http://oeis.org/A003154</a> in OEIS), the numbers of balls needed to form a six-pointed start of certain size. After this one had only to code the formula — <span class=\"tex-span\"><i>S</i><sub class=\"lower-index\"><i>n</i></sub> = 6<i>n</i>(<i>n</i>−1) + 1</span>.</p><h4><a href=\"/contest/171/problem/D\" title=\"April Fools Day Contest\">171D - Broken checker</a></h4><p>What does one do if the statement is unknown and the only source of information about the problem is the checker? Right — you just try all possible functions which convert 5 input values into 3 output values and see which of them fits :-)</p><h4><a href=\"/contest/171/problem/F\" title=\"April Fools Day Contest\">171F - ucyhf</a></h4><p>This problem finally has a statement! The trick is, it's encoded. We decided to be kind to you and to use the simplest cipher possible — Caesar cipher (each letter is shifted the same number of positions in the alphabet). By a long stretch of imagination one could break the cipher by hand — observe frequent letters and short words, deduce possible values of shift and verify it against the rest of the message. A lazier one could Google for a tool like <a href=\"http://www.sccs.swarthmore.edu/users/03/julieg/hw14cipher.html\">this one</a> and get the decoded version semi-automatically.</p><p>After cracking the statement the rest was almost easy — you had to find a prime whose reverse is a prime different from the original one (sequence <a href=\"http://oeis.org/A006567)\">http://oeis.org/A006567)</a>. 11184-th such number equals 999983, so one could do a brute-force check of all numbers in row.</p><h4><a href=\"/contest/171/problem/E\" title=\"April Fools Day Contest\">171E - MYSTERIOUS LANGUAGE</a></h4><p>A special contest written by me and no special programming language? Impossible! I pulled myself up and made only 25% of all problems esoteric — that's two. There really should be three but the third interpreter refused to cooperate. Maybe next time...</p><p>What can one do if all he knows about the language is its compiler? Just run any code and see what the compiler says. In this case the compiler said "DO YOU EXPECT ME TO FIGURE THIS OUT?", and Google should tell you immediately that the language in question is <a href=\"http://progopedia.com/language/intercal/\">INTERCAL</a>. The problem simplifies to figure out the dialect used and how to output "INTERCAL" in it.</p><p>In Codeforces round #96 I gave a problem <a href=\"/contest/133/problem/C\" title=\"Codeforces Beta Round 96 (Div. 2)\">133C - Turing Tape</a> which explained the mechanism of string output in INTERCAL and asked to write a program which converted a string into an array of numbers which would print this string. Combine this knowledge with <a href=\"http://progopedia.com/example/hello-world/257/\">Hello, World! example</a> and you get the program you need. Actually, that's what I did to write the reference solution.</p> <pre><code>PLEASE DO ,1 <- #8\nDO ,1 SUB #1 <- #110\nPLEASE DO ,1 SUB #2 <- #32\nDO ,1 SUB #3 <- #72\nDO ,1 SUB #4 <- #136\nDO ,1 SUB #5 <- #88\nDO ,1 SUB #6 <- #136\nDO ,1 SUB #7 <- #64\nDO ,1 SUB #8 <- #80\nPLEASE READ OUT ,1\nPLEASE GIVE UP\n</code></pre><h4><a href=\"/contest/171/problem/C\" title=\"April Fools Day Contest\">171C - A Piece of Cake</a></h4><p>The second esoteric problem had a <a href=\"http://progopedia.com/language/chef/\">Chef</a> program as the statement. You had only to figure out what it does and do it in any regular language. It turns out that this program reads N followed by N numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>N</i></sub></span> and calculated the sum <span class=\"tex-span\"><i>i</i> * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><h4><a href=\"/contest/171/problem/G\" title=\"April Fools Day Contest\">171G - Mysterious numbers - 2</a></h4><p>This one was much harder to guess but much easier to code. First two numbers were the start of a Fibonacci-like sequence, and the third one was the index of the required number in this sequence.</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/171\" class=\"notice\" style=\"text-decoration: none;\">April Fools Day Contest</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5202-4269\").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: \"5202\",\n blogEntryId: \"4255\",\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=april+1st\" class=\"tag notice\" style=\"text-decoration: none;\">april 1st</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-4269\"><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'>+48</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4269\"><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/Nickolas\"><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/Nickolas\">\n Nickolas\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=\"Apr/01/2012 21:01\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4255#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/4255#comments\">\n 5\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=\"4279\">\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 <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=\"86515\" 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/pencil_man\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/18809/avatar/c23f10f0e3e1c4ea.jpg'/> </a>\n <div><a href=\"/profile/pencil_man\" title=\"Expert pencil_man\" class=\"rated-user user-blue\">pencil_man</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/03/2012 05:55\">12 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-86515\" href=\"?#comment-86515\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"86515\" 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=\"86515\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"18809\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-86515\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><pre>.</pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-86515 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-86515 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-86515\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"86592\" commentParentId=\"86515\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ksun48\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.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:5px;right:10px'/> </a>\n <div><a href=\"/profile/ksun48\" title=\"International Grandmaster ksun48\" class=\"rated-user user-red\">ksun48</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/03/2012 19:52\">12 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-86592\" href=\"?#comment-86592\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-86515\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"86592\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"39840\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-86592\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Will there be an editorial for problem H?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-86592 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-86592 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-86592\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"86595\" commentParentId=\"86592\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/maksay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/440/avatar/e2a6dfc626509679.jpg'/> </a>\n <div><a href=\"/profile/maksay\" title=\"Master maksay\" class=\"rated-user user-orange\">maksay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/03/2012 20:24\">12 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-86595\" href=\"?#comment-86595\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-86592\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"86595\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"440\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-86595\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry, I left a comment in Russian and forgot to leave the same in English interface. Here it goes:</p><p>Problem H</p><p>You had to find the coordinates of a point that is situated on a given distance from the beginning of Hilbert curve of given order. It is known that length of Hilbert curve of order n is <span class=\"tex-span\">2<sup class=\"upper-index\">2 * <i>n</i></sup> - 1</span>. You could iterate through all orders of the curve from the biggest to the smallest and if the distance we still have to go is more than or equal to the length of a curve of a given order, we had to draw a curve of a given order and relocate from the beginning to the end. The only thing left is to learn how to find where will we be if we draw a curve of a given order rotated by some angle of 90 * k degrees. It is described, as well as the whole solution, in the <a href=\"https://en.wikipedia.org/wiki/Hilbert_curve\">Wikipedia</a>.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-86595 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-86595 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-86595\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"86924\" commentParentId=\"86595\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/ksun48\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.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:5px;right:10px'/> </a>\n <div><a href=\"/profile/ksun48\" title=\"International Grandmaster ksun48\" class=\"rated-user user-red\">ksun48</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/06/2012 00:50\">12 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-86924\" href=\"?#comment-86924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-86595\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"86924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"39840\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-86924\">\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-86924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-86924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-86924\">\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=\"163325\" 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/Daydreamer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41048/avatar/555a2d9e9ef2291c.jpg'/> </a>\n <div><a href=\"/profile/Daydreamer\" title=\"Pupil Daydreamer\" class=\"rated-user user-green\">Daydreamer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/01/2014 09:30\">10 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-163325\" href=\"?#comment-163325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"163325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41048\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-163325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe people like to read this tonight xD</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-163325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-163325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-163325\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4279\" 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Phone Code"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Phone Code</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>Polycarpus has <span class=\"tex-span\"><i>n</i></span> friends in Tarasov city. Polycarpus knows phone numbers of all his friends: they are strings <span class=\"tex-span\"><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>. All these strings consist only of digits and have the same length. </p><p>Once Polycarpus needed to figure out Tarasov city phone code. He assumed that the phone code of the city is the longest common prefix of all phone numbers of his friends. In other words, it is the longest string <span class=\"tex-span\"><i>c</i></span> which is a prefix (the beginning) of each <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> for all <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>). Help Polycarpus determine the length of the city phone code. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 3·10<sup class=\"upper-index\">4</sup></span>) — the number of Polycarpus's friends. The following <span class=\"tex-span\"><i>n</i></span> lines contain strings <span class=\"tex-span\"><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> — the phone numbers of Polycarpus's friends. It is guaranteed that all strings consist only of digits and have the same length from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">20</span>, inclusive. It is also guaranteed that all strings are different.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the number of digits in the city phone code.</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/>00209<br/>00219<br/>00999<br/>00909<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>2<br/>1<br/>2<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/>77012345678999999999<br/>77012345678901234567<br/>77012345678998765432<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>12<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>A <span class=\"tex-font-style-underline\">prefix</span> of string <span class=\"tex-span\"><i>t</i></span> is a string that is obtained by deleting zero or more digits from the end of string <span class=\"tex-span\"><i>t</i></span>. For example, string \"<span class=\"tex-font-style-tt\">00209</span>\" has 6 prefixes: \"\" (an empty prefix), \"<span class=\"tex-font-style-tt\">0</span>\", \"<span class=\"tex-font-style-tt\">00</span>\", \"<span class=\"tex-font-style-tt\">002</span>\", \"<span class=\"tex-font-style-tt\">0020</span>\", \"<span class=\"tex-font-style-tt\">00209</span>\".</p><p>In the first sample the city phone code is string \"<span class=\"tex-font-style-tt\">00</span>\".</p><p>In the second sample the city phone code is an empty string.</p><p>In the third sample the city phone code is string \"<span class=\"tex-font-style-tt\">770123456789</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=\"4b24654505ee26757348ac40fa2a7dc3\"/>\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=\"7735d65d40c2ecb86802cc17bd03ba1457265081\"/>\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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< 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_768f79cfcdee1958102af98c7b9c18c4123a5d5b\">\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. Phone Code</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>Polycarpus has <span class=\"tex-span\"><i>n</i></span> friends in Tarasov city. Polycarpus knows phone numbers of all his friends: they are strings <span class=\"tex-span\"><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>. All these strings consist only of digits and have the same length. </p><p>Once Polycarpus needed to figure out Tarasov city phone code. He assumed that the phone code of the city is the longest common prefix of all phone numbers of his friends. In other words, it is the longest string <span class=\"tex-span\"><i>c</i></span> which is a prefix (the beginning) of each <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> for all <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>). Help Polycarpus determine the length of the city phone code. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 3·10<sup class=\"upper-index\">4</sup></span>) — the number of Polycarpus's friends. The following <span class=\"tex-span\"><i>n</i></span> lines contain strings <span class=\"tex-span\"><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> — the phone numbers of Polycarpus's friends. It is guaranteed that all strings consist only of digits and have the same length from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">20</span>, inclusive. It is also guaranteed that all strings are different.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the number of digits in the city phone code.</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 />00209<br />00219<br />00999<br />00909<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>2<br />1<br />2<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 />77012345678999999999<br />77012345678901234567<br />77012345678998765432<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>12<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>A <span class=\"tex-font-style-underline\">prefix</span> of string <span class=\"tex-span\"><i>t</i></span> is a string that is obtained by deleting zero or more digits from the end of string <span class=\"tex-span\"><i>t</i></span>. For example, string "<span class=\"tex-font-style-tt\">00209</span>" has 6 prefixes: "" (an empty prefix), "<span class=\"tex-font-style-tt\">0</span>", "<span class=\"tex-font-style-tt\">00</span>", "<span class=\"tex-font-style-tt\">002</span>", "<span class=\"tex-font-style-tt\">0020</span>", "<span class=\"tex-font-style-tt\">00209</span>".</p><p>In the first sample the city phone code is string "<span class=\"tex-font-style-tt\">00</span>".</p><p>In the second sample the city phone code is an empty string.</p><p>In the third sample the city phone code is string "<span class=\"tex-font-style-tt\">770123456789</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 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\"*800\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":842,"cells":{"problem_id":{"kind":"string","value":"172B"},"contest":{"kind":"string","value":"172"},"problem":{"kind":"string","value":"B"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B. Pseudorandom Sequence Period"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Pseudorandom Sequence Period</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>Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1505a2bb013efb7ab20b04ab4c345c19fef97ccb.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> (for <span class=\"tex-span\"><i>i</i> ≥ 1</span>). Here <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>m</i></span> are constants, fixed for the given realization of the pseudorandom numbers generator, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span> is the so-called <span class=\"tex-span\"><i>randseed</i></span> (this value can be set from the program using functions like <span class=\"tex-font-style-tt\">RandSeed(r)</span> or <span class=\"tex-font-style-tt\">srand(n)</span>), and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e91a39ad64cd7a33e8f1b67cd60e5b40257de950.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> denotes the operation of taking the remainder of division.</p><p>For example, if <span class=\"tex-span\"><i>a</i> = 2, <i>b</i> = 6, <i>m</i> = 12, <i>r</i><sub class=\"lower-index\">0</sub> = 11</span>, the generated sequence will be: <span class=\"tex-span\">4, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, ...</span>.</p><p>Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.</p><p>Your task is to find the period of a sequence defined by the given values of <span class=\"tex-span\"><i>a</i>, <i>b</i>, <i>m</i></span> and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span>. Formally, you have to find such minimum positive integer <span class=\"tex-span\"><i>t</i></span>, for which exists such positive integer <span class=\"tex-span\"><i>k</i></span>, that for any <span class=\"tex-span\"><i>i</i> ≥ <i>k</i></span>: <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub> = <i>r</i><sub class=\"lower-index\"><i>i</i> + <i>t</i></sub></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains four integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup>, 0 ≤ <i>a</i>, <i>b</i> ≤ 1000, 0 ≤ <i>r</i><sub class=\"lower-index\">0</sub> < <i>m</i></span>), separated by single spaces.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the period of the sequence.</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 6 12 11<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>2 3 5 1<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>3 6 81 9<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>The first sample is described above. </p><p>In the second sample the sequence is (starting from the first element): <span class=\"tex-span\">0, 3, 4, 1, 0, 3, 4, 1, 0, ...</span></p><p>In the third sample the sequence is (starting from the first element): <span class=\"tex-span\">33, 24, 78, 78, 78, 78, ...</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=\"5a379e2f8501597d675db0347df136c4\"/>\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=\"7735d65d40c2ecb86802cc17bd03ba1457265081\"/>\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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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_58056f108f5cd05958d993b2fc1c99fdf77a3967\">\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. Pseudorandom Sequence Period</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>Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1505a2bb013efb7ab20b04ab4c345c19fef97ccb.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (for <span class=\"tex-span\"><i>i</i> ≥ 1</span>). Here <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>m</i></span> are constants, fixed for the given realization of the pseudorandom numbers generator, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span> is the so-called <span class=\"tex-span\"><i>randseed</i></span> (this value can be set from the program using functions like <span class=\"tex-font-style-tt\">RandSeed(r)</span> or <span class=\"tex-font-style-tt\">srand(n)</span>), and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e91a39ad64cd7a33e8f1b67cd60e5b40257de950.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> denotes the operation of taking the remainder of division.</p><p>For example, if <span class=\"tex-span\"><i>a</i> = 2, <i>b</i> = 6, <i>m</i> = 12, <i>r</i><sub class=\"lower-index\">0</sub> = 11</span>, the generated sequence will be: <span class=\"tex-span\">4, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, ...</span>.</p><p>Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.</p><p>Your task is to find the period of a sequence defined by the given values of <span class=\"tex-span\"><i>a</i>, <i>b</i>, <i>m</i></span> and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span>. Formally, you have to find such minimum positive integer <span class=\"tex-span\"><i>t</i></span>, for which exists such positive integer <span class=\"tex-span\"><i>k</i></span>, that for any <span class=\"tex-span\"><i>i</i> ≥ <i>k</i></span>: <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub> = <i>r</i><sub class=\"lower-index\"><i>i</i> + <i>t</i></sub></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains four integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">0</sub></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup>, 0 ≤ <i>a</i>, <i>b</i> ≤ 1000, 0 ≤ <i>r</i><sub class=\"lower-index\">0</sub> < <i>m</i></span>), separated by single spaces.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the period of the sequence.</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 6 12 11<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>2 3 5 1<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>3 6 81 9<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>The first sample is described above. </p><p>In the second sample the sequence is (starting from the first element): <span class=\"tex-span\">0, 3, 4, 1, 0, 3, 4, 1, 0, ...</span></p><p>In the third sample the sequence is (starting from 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{document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"},"long_tags":{"kind":"string","value":"[\"Special solving requirements, e.g. unknown programming language, etc.\", \"Implementation problems, programming technics, simulation\", \"Number theory: Euler function, GCD, divisibility, etc\"]"},"short_tags":{"kind":"string","value":"[\"*special problem\", \"implementation\", \"number theory\", \"*1200\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":843,"cells":{"problem_id":{"kind":"string","value":"172C"},"contest":{"kind":"string","value":"172"},"problem":{"kind":"string","value":"C"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"C. Bus"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Bus</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 bus stop near the university. The lessons are over, and <span class=\"tex-span\"><i>n</i></span> students come to the stop. The <span class=\"tex-span\"><i>i</i></span>-th student will appear at the bus stop at time <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (all <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>'s are distinct).</p><p>We shall assume that the stop is located on the coordinate axis <span class=\"tex-span\"><i>Ox</i></span>, at point <span class=\"tex-span\"><i>x</i> = 0</span>, and the bus goes along the ray <span class=\"tex-span\"><i>Ox</i></span>, that is, towards the positive direction of the coordinate axis, and back. The <span class=\"tex-span\"><i>i</i></span>-th student needs to get to the point with coordinate <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span>).</p><p>The bus moves by the following algorithm. Initially it is at point 0. The students consistently come to the stop and get on it. The bus has a seating capacity which is equal to <span class=\"tex-span\"><i>m</i></span> passengers. At the moment when <span class=\"tex-span\"><i>m</i></span> students get on the bus, it starts moving in the positive direction of the coordinate axis. Also it starts moving when the last (<span class=\"tex-span\"><i>n</i></span>-th) student gets on the bus. The bus is moving at a speed of 1 unit of distance per 1 unit of time, i.e. it covers distance <span class=\"tex-span\"><i>y</i></span> in time <span class=\"tex-span\"><i>y</i></span>.</p><p>Every time the bus passes the point at which at least one student needs to get off, it stops and these students get off the bus. The students need <span class=\"tex-span\">1 + [<i>k</i> / 2]</span> units of time to get off the bus, where <span class=\"tex-span\"><i>k</i></span> is the number of students who leave at this point. Expression <span class=\"tex-span\">[<i>k</i> / 2]</span> denotes rounded down <span class=\"tex-span\"><i>k</i> / 2</span>. As soon as the last student leaves the bus, the bus turns around and goes back to the point <span class=\"tex-span\"><i>x</i> = 0</span>. It doesn't make any stops until it reaches the point. At the given point the bus fills with students once more, and everything is repeated.</p><p>If students come to the stop when there's no bus, they form a line (queue) and get on the bus in the order in which they came. Any number of students get on the bus in negligible time, you should assume that it doesn't take any time. Any other actions also take no time. The bus has no other passengers apart from the students.</p><p>Write a program that will determine for each student the time when he got off the bus. The moment a student got off the bus is the moment the bus stopped at the student's destination stop (despite the fact that the group of students need some time to get off).</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>, <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 students and the number of passengers the bus can transport, correspondingly. Next <span class=\"tex-span\"><i>n</i></span> lines contain descriptions of the students, one per line. Each line contains a pair of integers <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub>, <i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>t</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">5</sup>, 1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>). The lines are given in the order of strict increasing of <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Values of <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> can coincide.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> numbers <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\">1</sub>, <i>w</i><sub class=\"lower-index\">2</sub>, ..., <i>w</i><sub class=\"lower-index\"><i>n</i></sub></span>, <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\"><i>i</i></sub></span> — the moment of time when the <span class=\"tex-span\"><i>i</i></span>-th student got off the bus. Print the numbers on one line and separate them with single spaces.</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 10<br/>3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1<br/>3 5<br/>4 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8 19<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>3 5<br/>4 5<br/>5 5<br/>6 5<br/>7 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>11 11 11 11 20<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>20 4<br/>28 13<br/>31 13<br/>35 6<br/>36 4<br/>52 6<br/>53 4<br/>83 2<br/>84 4<br/>87 1<br/>93 6<br/>108 4<br/>113 6<br/>116 1<br/>125 2<br/>130 2<br/>136 13<br/>162 2<br/>166 4<br/>184 1<br/>192 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>51 51 43 40 93 89 86 89 114 121 118 121 137 139 139 152 195 199 193 195<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the bus waits for the first student for <span class=\"tex-span\">3</span> units of time and drives him to his destination in additional <span class=\"tex-span\">5</span> units of time. So the student leaves the bus at the moment of time <span class=\"tex-span\">3 + 5 = 8</span>.</p><p>In the second sample the capacity of the bus equals <span class=\"tex-span\">1</span>, that's why it will drive the first student alone. This student is the same as the student from the first sample. So the bus arrives to his destination at the moment of time <span class=\"tex-span\">8</span>, spends <span class=\"tex-span\">1 + [1 / 2] = 1</span> units of time on getting him off, and returns back to <span class=\"tex-span\">0</span> in additional <span class=\"tex-span\">5</span> units of time. That is, the bus returns to the bus stop at the moment of time <span class=\"tex-span\">14</span>. By this moment the second student has already came to the bus stop. So he immediately gets in the bus, and is driven to his destination in additional <span class=\"tex-span\">5</span> units of time. He gets there at the moment <span class=\"tex-span\">14 + 5 = 19</span>. </p><p>In the third sample the bus waits for the fourth student for <span class=\"tex-span\">6</span> units of time, then drives for <span class=\"tex-span\">5</span> units of time, then gets the passengers off for <span class=\"tex-span\">1 + [4 / 2] = 3</span> units of time, then returns for <span class=\"tex-span\">5</span> units of time, and then drives the fifth student for <span class=\"tex-span\">1</span> unit of time.</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=\"be9f6bf322f550c2175f788c39e89697\"/>\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 - 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=\"7735d65d40c2ecb86802cc17bd03ba1457265081\"/>\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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< 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_18173a72574df0dfe99a7d45ab3b8b72f79e1a8b\">\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. Bus</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 bus stop near the university. The lessons are over, and <span class=\"tex-span\"><i>n</i></span> students come to the stop. The <span class=\"tex-span\"><i>i</i></span>-th student will appear at the bus stop at time <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (all <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>'s are distinct).</p><p>We shall assume that the stop is located on the coordinate axis <span class=\"tex-span\"><i>Ox</i></span>, at point <span class=\"tex-span\"><i>x</i> = 0</span>, and the bus goes along the ray <span class=\"tex-span\"><i>Ox</i></span>, that is, towards the positive direction of the coordinate axis, and back. The <span class=\"tex-span\"><i>i</i></span>-th student needs to get to the point with coordinate <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span>).</p><p>The bus moves by the following algorithm. Initially it is at point 0. The students consistently come to the stop and get on it. The bus has a seating capacity which is equal to <span class=\"tex-span\"><i>m</i></span> passengers. At the moment when <span class=\"tex-span\"><i>m</i></span> students get on the bus, it starts moving in the positive direction of the coordinate axis. Also it starts moving when the last (<span class=\"tex-span\"><i>n</i></span>-th) student gets on the bus. The bus is moving at a speed of 1 unit of distance per 1 unit of time, i.e. it covers distance <span class=\"tex-span\"><i>y</i></span> in time <span class=\"tex-span\"><i>y</i></span>.</p><p>Every time the bus passes the point at which at least one student needs to get off, it stops and these students get off the bus. The students need <span class=\"tex-span\">1 + [<i>k</i> / 2]</span> units of time to get off the bus, where <span class=\"tex-span\"><i>k</i></span> is the number of students who leave at this point. Expression <span class=\"tex-span\">[<i>k</i> / 2]</span> denotes rounded down <span class=\"tex-span\"><i>k</i> / 2</span>. As soon as the last student leaves the bus, the bus turns around and goes back to the point <span class=\"tex-span\"><i>x</i> = 0</span>. It doesn't make any stops until it reaches the point. At the given point the bus fills with students once more, and everything is repeated.</p><p>If students come to the stop when there's no bus, they form a line (queue) and get on the bus in the order in which they came. Any number of students get on the bus in negligible time, you should assume that it doesn't take any time. Any other actions also take no time. The bus has no other passengers apart from the students.</p><p>Write a program that will determine for each student the time when he got off the bus. The moment a student got off the bus is the moment the bus stopped at the student's destination stop (despite the fact that the group of students need some time to get off).</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>, <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 students and the number of passengers the bus can transport, correspondingly. Next <span class=\"tex-span\"><i>n</i></span> lines contain descriptions of the students, one per line. Each line contains a pair of integers <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub>, <i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>t</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">5</sup>, 1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>). The lines are given in the order of strict increasing of <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Values of <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> can coincide.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> numbers <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\">1</sub>, <i>w</i><sub class=\"lower-index\">2</sub>, ..., <i>w</i><sub class=\"lower-index\"><i>n</i></sub></span>, <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\"><i>i</i></sub></span> — the moment of time when the <span class=\"tex-span\"><i>i</i></span>-th student got off the bus. Print the numbers on one line and separate them with single spaces.</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 10<br />3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1<br />3 5<br />4 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8 19<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />3 5<br />4 5<br />5 5<br />6 5<br />7 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>11 11 11 11 20<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>20 4<br />28 13<br />31 13<br />35 6<br />36 4<br />52 6<br />53 4<br />83 2<br />84 4<br />87 1<br />93 6<br />108 4<br />113 6<br />116 1<br />125 2<br />130 2<br />136 13<br />162 2<br />166 4<br />184 1<br />192 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>51 51 43 40 93 89 86 89 114 121 118 121 137 139 139 152 195 199 193 195<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the bus waits for the first student for <span class=\"tex-span\">3</span> units of time and drives him to his destination in additional <span class=\"tex-span\">5</span> units of time. So the student leaves the bus at the moment of time <span class=\"tex-span\">3 + 5 = 8</span>.</p><p>In the second sample the capacity of the bus equals <span class=\"tex-span\">1</span>, that's why it will drive the first student alone. This student is the same as the student from the first sample. So the bus arrives to his destination at the moment of time <span class=\"tex-span\">8</span>, spends <span class=\"tex-span\">1 + [1 / 2] = 1</span> units of time on getting him off, and returns back to <span class=\"tex-span\">0</span> in additional <span class=\"tex-span\">5</span> units of time. That is, the bus returns to the bus stop at the moment of time <span class=\"tex-span\">14</span>. By this moment the second student has already came to the bus stop. So he immediately gets in the bus, and is driven to his destination in additional <span class=\"tex-span\">5</span> units of time. He gets there at the moment <span class=\"tex-span\">14 + 5 = 19</span>. </p><p>In the third sample the bus waits for the fourth student for <span class=\"tex-span\">6</span> units of time, then drives for <span class=\"tex-span\">5</span> units of time, then gets the passengers off for <span class=\"tex-span\">1 + [4 / 2] = 3</span> units of time, then returns for <span class=\"tex-span\">5</span> units of time, and then drives the fifth student for <span class=\"tex-span\">1</span> unit of time.</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 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\"*1500\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":844,"cells":{"problem_id":{"kind":"string","value":"172D"},"contest":{"kind":"string","value":"172"},"problem":{"kind":"string","value":"D"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"D. Calendar Reform"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Calendar Reform</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>Reforms have started in Berland again! At this time, the Parliament is discussing the reform of the calendar. To make the lives of citizens of Berland more varied, it was decided to change the calendar. As more and more people are complaining that \"the years fly by...\", it was decided that starting from the next year the number of days per year will begin to grow. So the coming year will have exactly <span class=\"tex-span\"><i>a</i></span> days, the next after coming year will have <span class=\"tex-span\"><i>a</i> + 1</span> days, the next one will have <span class=\"tex-span\"><i>a</i> + 2</span> days and so on. This schedule is planned for the coming <span class=\"tex-span\"><i>n</i></span> years (in the <span class=\"tex-span\"><i>n</i></span>-th year the length of the year will be equal <span class=\"tex-span\"><i>a</i> + <i>n</i> - 1</span> day).</p><p>No one has yet decided what will become of months. An MP Palevny made the following proposal. </p><ul> <li> The calendar for each month is comfortable to be printed on a square sheet of paper. We are proposed to make the number of days in each month be the square of some integer. The number of days per month should be the same for each month of any year, but may be different for different years. </li><li> The number of days in each year must be divisible by the number of days per month in this year. This rule ensures that the number of months in each year is an integer. </li><li> The number of days per month for each year must be chosen so as to save the maximum amount of paper to print the calendars. In other words, the number of days per month should be as much as possible. </li></ul><p>These rules provide an unambiguous method for choosing the number of days in each month for any given year length. For example, according to Palevny's proposition, a year that consists of 108 days will have three months, 36 days each. The year that consists of 99 days will have 11 months, 9 days each, and a year of 365 days will have 365 months, one day each.</p><p>The proposal provoked heated discussion in the community, the famous mathematician Perelmanov quickly calculated that if the proposal is supported, then in a period of <span class=\"tex-span\"><i>n</i></span> years, beginning with the year that has <span class=\"tex-span\"><i>a</i></span> days, the country will spend <span class=\"tex-span\"><i>p</i></span> sheets of paper to print a set of calendars for these years. Perelmanov's calculations take into account the fact that the set will contain one calendar for each year and each month will be printed on a separate sheet.</p><p>Repeat Perelmanov's achievement and print the required number <span class=\"tex-span\"><i>p</i></span>. You are given positive integers <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>n</i></span>. Perelmanov warns you that your program should not work longer than four seconds at the maximum test.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only input line contains a pair of integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>a</i>, <i>n</i> ≤ 10<sup class=\"upper-index\">7</sup>;</span> <span class=\"tex-span\"><i>a</i> + <i>n</i> - 1 ≤ 10<sup class=\"upper-index\">7</sup></span>).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the required number <span class=\"tex-span\"><i>p</i></span>. </p><p>Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use cin, cout streams or the %I64d 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>25 3<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>50 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>125<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>A note to the first sample test. A year of 25 days will consist of one month containing 25 days. A year of 26 days will consist of 26 months, one day each. 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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_2ecb2797d12ea1f382a9d813a870c98cc1918099\">\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. Calendar Reform</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>Reforms have started in Berland again! At this time, the Parliament is discussing the reform of the calendar. To make the lives of citizens of Berland more varied, it was decided to change the calendar. As more and more people are complaining that "the years fly by...", it was decided that starting from the next year the number of days per year will begin to grow. So the coming year will have exactly <span class=\"tex-span\"><i>a</i></span> days, the next after coming year will have <span class=\"tex-span\"><i>a</i> + 1</span> days, the next one will have <span class=\"tex-span\"><i>a</i> + 2</span> days and so on. This schedule is planned for the coming <span class=\"tex-span\"><i>n</i></span> years (in the <span class=\"tex-span\"><i>n</i></span>-th year the length of the year will be equal <span class=\"tex-span\"><i>a</i> + <i>n</i> - 1</span> day).</p><p>No one has yet decided what will become of months. An MP Palevny made the following proposal. </p><ul> <li> The calendar for each month is comfortable to be printed on a square sheet of paper. We are proposed to make the number of days in each month be the square of some integer. The number of days per month should be the same for each month of any year, but may be different for different years. </li><li> The number of days in each year must be divisible by the number of days per month in this year. This rule ensures that the number of months in each year is an integer. </li><li> The number of days per month for each year must be chosen so as to save the maximum amount of paper to print the calendars. In other words, the number of days per month should be as much as possible. </li></ul><p>These rules provide an unambiguous method for choosing the number of days in each month for any given year length. For example, according to Palevny's proposition, a year that consists of 108 days will have three months, 36 days each. The year that consists of 99 days will have 11 months, 9 days each, and a year of 365 days will have 365 months, one day each.</p><p>The proposal provoked heated discussion in the community, the famous mathematician Perelmanov quickly calculated that if the proposal is supported, then in a period of <span class=\"tex-span\"><i>n</i></span> years, beginning with the year that has <span class=\"tex-span\"><i>a</i></span> days, the country will spend <span class=\"tex-span\"><i>p</i></span> sheets of paper to print a set of calendars for these years. Perelmanov's calculations take into account the fact that the set will contain one calendar for each year and each month will be printed on a separate sheet.</p><p>Repeat Perelmanov's achievement and print the required number <span class=\"tex-span\"><i>p</i></span>. You are given positive integers <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>n</i></span>. Perelmanov warns you that your program should not work longer than four seconds at the maximum test.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only input line contains a pair of integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>a</i>, <i>n</i> ≤ 10<sup class=\"upper-index\">7</sup>;</span> <span class=\"tex-span\"><i>a</i> + <i>n</i> - 1 ≤ 10<sup class=\"upper-index\">7</sup></span>).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the required number <span class=\"tex-span\"><i>p</i></span>. </p><p>Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use cin, cout streams or the %I64d 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>25 3<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>50 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>125<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>A note to the first sample test. A year of 25 days will consist of one month containing 25 days. A year of 26 days will consist of 26 months, one day each. A year of 27 days will have three months, 9 days each.</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: previousStatementText, b: statementText}, function (result) {\r\n if (result[\"success\"] === \"true\") {\r\n Codeforces.facebox(\".diff-popup\", 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BHTML+BCSS"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. BHTML+BCSS</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><span class=\"tex-font-style-it\">This problem is about imaginary languages BHTML and BCSS, which slightly resemble HTML and CSS. Read the problem statement carefully as the resemblance is rather slight and the problem uses very simplified analogs.</span></p><p>You are given a BHTML document that resembles HTML but is much simpler. It is recorded as a sequence of opening and closing tags. A tag that looks like \"<span class=\"tex-font-style-tt\"><tagname></span>\" is called an opening tag and a tag that looks like \"<span class=\"tex-font-style-tt\"></tagname></span>\" is called a closing tag. Besides, there are self-closing tags that are written as \"<span class=\"tex-font-style-tt\"><tagname/></span>\" and in this problem they are fully equivalent to \"<span class=\"tex-font-style-tt\"><tagname></tagname></span>\". All tagnames in this problem are strings consisting of lowercase Latin letters with length from 1 to 10 characters. Tagnames of different tags may coincide.</p><p>The document tags form a correct bracket sequence, that is, we can obtain an empty sequence from the given one using the following operations: </p><ul> <li> remove any self-closing tag \"<span class=\"tex-font-style-tt\"><tagname/></span>\", </li><li> remove a pair of an opening and a closing tag that go consecutively (in this order) and have the same names. In other words, remove substring \"<span class=\"tex-font-style-tt\"><tagname></tagname></span>\". </li></ul><p>For example, you may be given such document: \"<span class=\"tex-font-style-tt\"><header><p><a/><b></b></p></header><footer></footer></span>\" but you may not be given documents \"<span class=\"tex-font-style-tt\"><a></span>\", \"<span class=\"tex-font-style-tt\"><a></b></span>\", \"<span class=\"tex-font-style-tt\"></a><a></span>\" or \"<span class=\"tex-font-style-tt\"><a><b></a></b></span>\".</p><p>Obviously, for any opening tag there is the only matching closing one — each such pair is called an <span class=\"tex-font-style-it\">element</span>. A self-closing tag also is an element. Let's consider that one element is nested inside another one, if tags of the first element are between tags of the second one. An element is not nested to itself. For instance, in the example above element \"<span class=\"tex-font-style-tt\">b</span>\" is nested in \"<span class=\"tex-font-style-tt\">header</span>\" and in \"<span class=\"tex-font-style-tt\">p</span>\", but it isn't nested in \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">footer</span>\", also it isn't nested to itself (\"<span class=\"tex-font-style-tt\">b</span>\"). Element \"<span class=\"tex-font-style-tt\">header</span>\" has three elements nested in it, and \"<span class=\"tex-font-style-tt\">footer</span>\" has zero.</p><p>We need the BCSS rules to apply styles when displaying elements of the BHTML documents. Each rule is recorded as a subsequence of words \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span> <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span> ... <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>\". This rule has effect over all such elements <span class=\"tex-span\"><i>t</i></span>, which satisfy both conditions from the list:</p><ul> <li> there is a sequence of nested elements with tagnames \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span></span>\", \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span></span>\", ..., \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>\" (that is, the second element is nested in the first one, the third element is nested in the second one and so on), </li><li> this sequence ends with element <span class=\"tex-span\"><i>t</i></span> (i.e. tagname of element <span class=\"tex-span\"><i>t</i></span> equals \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>\"). </li></ul><p>For example, element \"<span class=\"tex-font-style-tt\">b</span>\" meets the conditions of the rule \"<span class=\"tex-font-style-tt\">a b</span>\" if for element \"<span class=\"tex-font-style-tt\">b</span>\" exists element \"<span class=\"tex-font-style-tt\">a</span>\" in which it is nested. Element \"<span class=\"tex-font-style-tt\">c</span>\" meets the conditions of the rule \"<span class=\"tex-font-style-tt\">a b b c</span>\", if three elements exist: \"<span class=\"tex-font-style-tt\">a</span>\", \"<span class=\"tex-font-style-tt\">b</span>\", \"<span class=\"tex-font-style-tt\">b</span>\", and in the chain \"<span class=\"tex-font-style-tt\">a</span>\"-\"<span class=\"tex-font-style-tt\">b</span>\"-\"<span class=\"tex-font-style-tt\">b</span>\"-\"<span class=\"tex-font-style-tt\">c</span>\" each following element is nested in the previous one.</p><p>Given a BHTML document and a set of BCSS rules, write a program that determines the number of elements that meet the conditions of each rule.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains a BHTML-document. The document has length from <span class=\"tex-span\">4</span> to <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span> characters. The document has a correct structure, doesn't contain spaces or any other unnecessary characters. Tagnames consist of lowercase Latin letters, their lengths are from 1 to 10 characters.</p><p>The second line contains an integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span>) — the number of queries. Then <span class=\"tex-span\"><i>m</i></span> lines contain the queries, one per line. Each query is a sequence <span class=\"tex-span\"><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>n</i></sub></span>, where <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th element of the query, and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span>) is the number of elements in the query. The elements are separated by single spaces. Each query doesn't begin with and doesn't end with a space. Each query element is a sequence of lowercase Latin letters with length from 1 to 10.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>m</i></span> lines, the <span class=\"tex-span\"><i>j</i></span>-th line should contain the number of elements of the document that correspond to the <span class=\"tex-span\"><i>j</i></span>-th BCSS-rule. If there are no such elements at all, print on the line <span class=\"tex-font-style-tt\">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><a><b><b></b></b></a><a><b></b><b><v/></b></a><b></b><br/>4<br/>a<br/>a b b<br/>a b<br/>b a<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>4<br/>0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre><b><aa/></b><aa><b/><b/></aa><br/>5<br/>aa b<br/>b<br/>aa<br/>b aa<br/>a<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>3<br/>2<br/>1<br/>0<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=\"0485e2d85d4006b8f0673124ba17ebc8\"/>\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=\"7735d65d40c2ecb86802cc17bd03ba1457265081\"/>\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='0485e2d85d4006b8f0673124ba17ebc8'/>\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/172/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=\"Special solving requirements, e.g. unknown programming language, etc.\">\r\n *special problem\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=\"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=\"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='0485e2d85d4006b8f0673124ba17ebc8'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1078\"/>\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='0485e2d85d4006b8f0673124ba17ebc8'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1078\"/>\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/4262\" title=\"Croc Champ 2012 — Qualification Round\" target=\"_blank\">Announcement</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"655:656\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/172\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/172/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/172/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/172/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/172/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/172/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=\"E\" data-uuid=\"ps_20db96a9e6abcc3c124aaa8bda8c02896a575d4e\">\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. BHTML+BCSS</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><span class=\"tex-font-style-it\">This problem is about imaginary languages BHTML and BCSS, which slightly resemble HTML and CSS. Read the problem statement carefully as the resemblance is rather slight and the problem uses very simplified analogs.</span></p><p>You are given a BHTML document that resembles HTML but is much simpler. It is recorded as a sequence of opening and closing tags. A tag that looks like "<span class=\"tex-font-style-tt\"><tagname></span>" is called an opening tag and a tag that looks like "<span class=\"tex-font-style-tt\"></tagname></span>" is called a closing tag. Besides, there are self-closing tags that are written as "<span class=\"tex-font-style-tt\"><tagname/></span>" and in this problem they are fully equivalent to "<span class=\"tex-font-style-tt\"><tagname></tagname></span>". All tagnames in this problem are strings consisting of lowercase Latin letters with length from 1 to 10 characters. Tagnames of different tags may coincide.</p><p>The document tags form a correct bracket sequence, that is, we can obtain an empty sequence from the given one using the following operations: </p><ul> <li> remove any self-closing tag "<span class=\"tex-font-style-tt\"><tagname/></span>", </li><li> remove a pair of an opening and a closing tag that go consecutively (in this order) and have the same names. In other words, remove substring "<span class=\"tex-font-style-tt\"><tagname></tagname></span>". </li></ul><p>For example, you may be given such document: "<span class=\"tex-font-style-tt\"><header><p><a/><b></b></p></header><footer></footer></span>" but you may not be given documents "<span class=\"tex-font-style-tt\"><a></span>", "<span class=\"tex-font-style-tt\"><a></b></span>", "<span class=\"tex-font-style-tt\"></a><a></span>" or "<span class=\"tex-font-style-tt\"><a><b></a></b></span>".</p><p>Obviously, for any opening tag there is the only matching closing one — each such pair is called an <span class=\"tex-font-style-it\">element</span>. A self-closing tag also is an element. Let's consider that one element is nested inside another one, if tags of the first element are between tags of the second one. An element is not nested to itself. For instance, in the example above element "<span class=\"tex-font-style-tt\">b</span>" is nested in "<span class=\"tex-font-style-tt\">header</span>" and in "<span class=\"tex-font-style-tt\">p</span>", but it isn't nested in "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">footer</span>", also it isn't nested to itself ("<span class=\"tex-font-style-tt\">b</span>"). Element "<span class=\"tex-font-style-tt\">header</span>" has three elements nested in it, and "<span class=\"tex-font-style-tt\">footer</span>" has zero.</p><p>We need the BCSS rules to apply styles when displaying elements of the BHTML documents. Each rule is recorded as a subsequence of words "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span> <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span> ... <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>". This rule has effect over all such elements <span class=\"tex-span\"><i>t</i></span>, which satisfy both conditions from the list:</p><ul> <li> there is a sequence of nested elements with tagnames "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span></span>", "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span></span>", ..., "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>" (that is, the second element is nested in the first one, the third element is nested in the second one and so on), </li><li> this sequence ends with element <span class=\"tex-span\"><i>t</i></span> (i.e. tagname of element <span class=\"tex-span\"><i>t</i></span> equals "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>n</i></sub></span></span>"). </li></ul><p>For example, element "<span class=\"tex-font-style-tt\">b</span>" meets the conditions of the rule "<span class=\"tex-font-style-tt\">a b</span>" if for element "<span class=\"tex-font-style-tt\">b</span>" exists element "<span class=\"tex-font-style-tt\">a</span>" in which it is nested. Element "<span class=\"tex-font-style-tt\">c</span>" meets the conditions of the rule "<span class=\"tex-font-style-tt\">a b b c</span>", if three elements exist: "<span class=\"tex-font-style-tt\">a</span>", "<span class=\"tex-font-style-tt\">b</span>", "<span class=\"tex-font-style-tt\">b</span>", and in the chain "<span class=\"tex-font-style-tt\">a</span>"-"<span class=\"tex-font-style-tt\">b</span>"-"<span class=\"tex-font-style-tt\">b</span>"-"<span class=\"tex-font-style-tt\">c</span>" each following element is nested in the previous one.</p><p>Given a BHTML document and a set of BCSS rules, write a program that determines the number of elements that meet the conditions of each rule.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains a BHTML-document. The document has length from <span class=\"tex-span\">4</span> to <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span> characters. The document has a correct structure, doesn't contain spaces or any other unnecessary characters. Tagnames consist of lowercase Latin letters, their lengths are from 1 to 10 characters.</p><p>The second line contains an integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span>) — the number of queries. Then <span class=\"tex-span\"><i>m</i></span> lines contain the queries, one per line. Each query is a sequence <span class=\"tex-span\"><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>n</i></sub></span>, where <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th element of the query, and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span>) is the number of elements in the query. The elements are separated by single spaces. Each query doesn't begin with and doesn't end with a space. Each query element is a sequence of lowercase Latin letters with length from 1 to 10.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>m</i></span> lines, the <span class=\"tex-span\"><i>j</i></span>-th line should contain the number of elements of the document that correspond to the <span class=\"tex-span\"><i>j</i></span>-th BCSS-rule. If there are no such elements at all, print on the line <span class=\"tex-font-style-tt\">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><a><b><b></b></b></a><a><b></b><b><v/></b></a><b></b><br />4<br />a<br />a b b<br />a b<br />b a<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />4<br />0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre><b><aa/></b><aa><b/><b/></aa><br />5<br />aa b<br />b<br />aa<br />b aa<br />a<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />3<br />2<br />1<br />0<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 = 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\"*2200\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":846,"cells":{"problem_id":{"kind":"string","value":"173A"},"contest":{"kind":"string","value":"173"},"problem":{"kind":"string","value":"A"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A. Rock-Paper-Scissors"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Rock-Paper-Scissors</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>Nikephoros and Polycarpus play rock-paper-scissors. The loser gets pinched (not too severely!).</p><p>Let us remind you the rules of this game. Rock-paper-scissors is played by two players. In each round the players choose one of three items independently from each other. They show the items with their hands: a rock, scissors or paper. The winner is determined by the following rules: the rock beats the scissors, the scissors beat the paper and the paper beats the rock. If the players choose the same item, the round finishes with a draw.</p><p>Nikephoros and Polycarpus have played <span class=\"tex-span\"><i>n</i></span> rounds. In each round the winner gave the loser a friendly pinch and the loser ended up with a fresh and new red spot on his body. If the round finished in a draw, the players did nothing and just played on.</p><p>Nikephoros turned out to have worked out the following strategy: before the game began, he chose some sequence of items <span class=\"tex-span\"><i>A</i> = (<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub>)</span>, and then he cyclically showed the items from this sequence, starting from the first one. Cyclically means that Nikephoros shows signs in the following order: <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\">...</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></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\">...</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\">...</span> and so on. Polycarpus had a similar strategy, only he had his own sequence of items <span class=\"tex-span\"><i>B</i> = (<i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>k</i></sub>)</span>.</p><p>Determine the number of red spots on both players after they've played <span class=\"tex-span\"><i>n</i></span> rounds of the game. You can consider that when the game began, the boys had no red spots on 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> ≤ 2·10<sup class=\"upper-index\">9</sup></span>) — the number of the game's rounds.</p><p>The second line contains sequence <span class=\"tex-span\"><i>A</i></span> as a string of <span class=\"tex-span\"><i>m</i></span> characters and the third line contains sequence <span class=\"tex-span\"><i>B</i></span> as a string of <span class=\"tex-span\"><i>k</i></span> characters (<span class=\"tex-span\">1 ≤ <i>m</i>, <i>k</i> ≤ 1000</span>). The given lines only contain characters \"<span class=\"tex-font-style-tt\">R</span>\", \"<span class=\"tex-font-style-tt\">S</span>\" and \"<span class=\"tex-font-style-tt\">P</span>\". Character \"<span class=\"tex-font-style-tt\">R</span>\" stands for the rock, character \"<span class=\"tex-font-style-tt\">S</span>\" represents the scissors and \"<span class=\"tex-font-style-tt\">P</span>\" represents the paper.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print two space-separated integers: the numbers of red spots Nikephoros and Polycarpus have.</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<br/>RPS<br/>RSPP<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3 2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>RRRRRRRR<br/>R<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 0</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the game went like this:</p><ul> <li> <span class=\"tex-font-style-tt\">R - R</span>. Draw. </li><li> <span class=\"tex-font-style-tt\">P - S</span>. Nikephoros loses. </li><li> <span class=\"tex-font-style-tt\">S - P</span>. Polycarpus loses. </li><li> <span class=\"tex-font-style-tt\">R - P</span>. Nikephoros loses. </li><li> <span class=\"tex-font-style-tt\">P - R</span>. Polycarpus loses. </li><li> <span class=\"tex-font-style-tt\">S - S</span>. Draw. </li><li> <span class=\"tex-font-style-tt\">R - P</span>. Nikephoros loses. </li></ul><p>Thus, in total Nikephoros has <span class=\"tex-span\">3</span> losses (and <span class=\"tex-span\">3</span> red spots), and Polycarpus only has <span class=\"tex-span\">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=\"9207a4307756fe5337f6567865a00893\"/>\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=\"5ffba53baf6e52414710ce740de55eabe4bff8cb\"/>\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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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_eb744e713bb9883d7f927240848847725f73d714\">\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. Rock-Paper-Scissors</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>Nikephoros and Polycarpus play rock-paper-scissors. The loser gets pinched (not too severely!).</p><p>Let us remind you the rules of this game. Rock-paper-scissors is played by two players. In each round the players choose one of three items independently from each other. They show the items with their hands: a rock, scissors or paper. The winner is determined by the following rules: the rock beats the scissors, the scissors beat the paper and the paper beats the rock. If the players choose the same item, the round finishes with a draw.</p><p>Nikephoros and Polycarpus have played <span class=\"tex-span\"><i>n</i></span> rounds. In each round the winner gave the loser a friendly pinch and the loser ended up with a fresh and new red spot on his body. If the round finished in a draw, the players did nothing and just played on.</p><p>Nikephoros turned out to have worked out the following strategy: before the game began, he chose some sequence of items <span class=\"tex-span\"><i>A</i> = (<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub>)</span>, and then he cyclically showed the items from this sequence, starting from the first one. Cyclically means that Nikephoros shows signs in the following order: <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\">...</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></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\">...</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\">...</span> and so on. Polycarpus had a similar strategy, only he had his own sequence of items <span class=\"tex-span\"><i>B</i> = (<i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>k</i></sub>)</span>.</p><p>Determine the number of red spots on both players after they've played <span class=\"tex-span\"><i>n</i></span> rounds of the game. You can consider that when the game began, the boys had no red spots on 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> ≤ 2·10<sup class=\"upper-index\">9</sup></span>) — the number of the game's rounds.</p><p>The second line contains sequence <span class=\"tex-span\"><i>A</i></span> as a string of <span class=\"tex-span\"><i>m</i></span> characters and the third line contains sequence <span class=\"tex-span\"><i>B</i></span> as a string of <span class=\"tex-span\"><i>k</i></span> characters (<span class=\"tex-span\">1 ≤ <i>m</i>, <i>k</i> ≤ 1000</span>). The given lines only contain characters "<span class=\"tex-font-style-tt\">R</span>", "<span class=\"tex-font-style-tt\">S</span>" and "<span class=\"tex-font-style-tt\">P</span>". Character "<span class=\"tex-font-style-tt\">R</span>" stands for the rock, character "<span class=\"tex-font-style-tt\">S</span>" represents the scissors and "<span class=\"tex-font-style-tt\">P</span>" represents the paper.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print two space-separated integers: the numbers of red spots Nikephoros and Polycarpus have.</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<br />RPS<br />RSPP<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3 2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />RRRRRRRR<br />R<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 0</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the game went like this:</p><ul> <li> <span class=\"tex-font-style-tt\">R - R</span>. Draw. </li><li> <span class=\"tex-font-style-tt\">P - S</span>. Nikephoros loses. </li><li> <span class=\"tex-font-style-tt\">S - P</span>. Polycarpus loses. </li><li> <span class=\"tex-font-style-tt\">R - P</span>. Nikephoros loses. </li><li> <span class=\"tex-font-style-tt\">P - R</span>. Polycarpus loses. </li><li> <span class=\"tex-font-style-tt\">S - S</span>. Draw. </li><li> <span class=\"tex-font-style-tt\">R - P</span>. 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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='3300ca74d4382dba1905b54116e2e886'/>\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)\" 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/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=\"4303\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4289\"> <p>Croc Champ 2012 — Round 1 — Editorial</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=\"Apr/06/2012 20:51\">12 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>A.</strong> Naive solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> (some simulation all of n rounds) gets TL. Let's speed up this solution. Let's consider rounds on segments [1..mk], [mk+1..2mk], [2mk+1..3mk] and so on. You can see that results of games on these segments will repeat. So you can simulate over exactly one segment and then take into consideration them [n/(mk)] times ([x] is rounding down). Remainder of n%(mk) last rounds you can simulate separately. So you have <span class=\"tex-span\"><i>O</i>(<i>mk</i>)</span> solution that easily fits into time limits.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a> and <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B.</strong> In this problem you should build bipartite graph with n+m vertices. All vertices of the firts part correspond to the rows of the table, vertices of the second part correspond to the columns of the one. Edge connects vertices iff some regular column is placed in the cross of corresponding row and column.</p><p>Firstly death ray covers only last row of the table that corresponds to one of vertices of our graph. When you are changing regular column into magic one, you are allowing death ray "go" by corresponding edge.</p><p>Now you can reformulate the statement by this way: "activate" minimal number of edges in biratrite graph, so some path of minimal lenght connects vertex of the last row of the table and vertex of the first row of the table.</p><p>You can see that required set of edges is just shortest path between these vertices. You can find this path using BFS. If BFS didn't find any path — answer is -1.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>((<i>n</i> + <i>m</i>)<sup class=\"upper-index\">2</sup>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/haas\" title=\"Candidate Master haas\">haas</a>.</p><p><strong>C.</strong> Let's iterate over all spirals and chose one of them that has maximal sum of elements. Because you have <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> spirals, you should calculate sum of any of them in <span class=\"tex-span\"><i>O</i>(1)</span>. Only in this case your solution will fit into time limits.</p><p>Let's define a way for iterate over all spirals. Let's fix one of cells and then iterate over all spirals that have own center in that cell in order of increasing side. So, you can recalculate sum for every spiral from previous one in <span class=\"tex-span\"><i>O</i>(1)</span> using following picture:</p><p><img alt=\" \" src=\"/predownloaded/c6/6c/c66c359162803c71990659a745c7a0c2e9e43683.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>For finding the first "summand", you should in the beginning calculate rectangular partial sums.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>D.</strong> You have bipartite graph with <span class=\"tex-span\">3<i>k</i></span> vertices and should to color its vertices by <span class=\"tex-span\"><i>k</i></span> colors. Every color should be used exactly 3 times and there should be no edges that connect vertices at same color.</p><p>At the first, you should find both of parts of our birartite graph using, for example, DFS. Now let's consider sizes of parts.</p><p>Case 0. If both of sizes divides by 3, you can just split every of parts into groups of 3 vertices and color them.</p><p>Otherwise we can note then size of the first part is 1 modulo 3 and size of the second part is 2 modulo 3.</p><p>There are yet another 2 cases:</p><p>Case 1. You should try to find one vertex from the firts part that have 2 "antiedges" to 2 different vertices of the second part. If you found it, you should color them and reduce the problem to case 0.</p><p>Case 2. There you should try to find 2 vertices on the second part. Every of them should have 2 "antiedges" that "connect" them with 4 different vertices trom the firts part. If you found such 6 vertices, you can color them by 2 different colors and reduce the problem to case 0.</p><p>If you doesn't find coloring using this cases, answer is NO.</p><p>About implementation: it is not clear how to analyse the case 2 in acceptable time. Actually, you can find any two vertices from the second part that have at least two "antiedges". These "antiedges" will conduct to 4 different vertices of the first part because otherwise case 1 would have worked.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span>.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>E.</strong> Let's transform all people into points on a plane with coordinates (<span class=\"tex-span\"><i>x</i> = <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i> = <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>). What the maximal number in group of people that can be formed with some fixed leader? Answer is number of points inside rectangle <span class=\"tex-span\">(<i>x</i>, <i>y</i>): <i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i> ≤ <i>x</i> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>y</i> ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Let's we allready found size of group for every person. How to find maximal group that contain points <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> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>j</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span> both? The required group should have leader with age in range from <span class=\"tex-span\"><i>max</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> - <i>k</i>)</span> то <span class=\"tex-span\"><i>min</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> + <i>k</i>)</span> and responsibility at least <span class=\"tex-span\"><i>max</i>(<i>y</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. From such leaders you should chose one that have maximal size of group. You can see that it is just query for maximum on some rectangle.</p><p>Well, let's learn to quickly find answers for queries of sums in rectangle. You should compress coordinates <span class=\"tex-span\"><i>x</i></span> ans build segment tree for sum. Then you should answer all queries in increasing order of coordinate <span class=\"tex-span\"><i>y</i></span>. When you consider some group with same <span class=\"tex-span\"><i>y</i></span>, you should initially do queries of adding values in points, and after that do sum queries on the segments from <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i></span> to <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i></span>.</p><p>Queries for maximum you can satisfy fully analogicaly using segment tree for maximum.</p><p>So, you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2cd1eac556a7b44fe282c5a5fdd92bc1f8fcd187.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> offline solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</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/173\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 1</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4303\").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: \"4289\",\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=croc\" class=\"tag notice\" style=\"text-decoration: none;\">croc</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012-round-1\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-1</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-4303\"><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'>+103</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4303\"><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=\"Apr/06/2012 20:51\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4289#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/4289#comments\">\n 3\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=\"4313\">\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 (2)</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=\"87322\" 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/P___\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/P___\" title=\"Expert P___\" class=\"rated-user user-blue\">P___</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/07/2012 23:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87322\" href=\"?#comment-87322\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87322\" class=\"CommentVoteFrame\"\r\n class=\"too-negative-comment-vote\"\r\n data-commentRating=\"-48\"\r\n data-commentUserId=\"333\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-48</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87322\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think that this contest was prepared badly. The point weight for task B should be 1500, it could be considered if task C is worth 1500 points too, I would vote for 1000. Because of this fault many coders didn't solve the third problem and waste a lot of time on the second one.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87322 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87322 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87322\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1047416\" 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/tan1shqc\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/tan1shqc\" title=\"Specialist tan1shqc\" class=\"rated-user user-cyan\">tan1shqc</a></div>\n </div>\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/15/2023 09:09\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1047416\" href=\"?#comment-1047416\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1047416\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2729268\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1047416\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>why does this TLE</p><p><a href=\"https://codeforces.com/problemset/submission/173/213861759\">https://codeforces.com/problemset/submission/173/213861759</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1047416 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1047416 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1047416\">\r\n 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Chamber of Secrets"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Chamber of Secrets</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 Chamber of Secrets has been opened again\" — this news has spread all around Hogwarts and some of the students have been petrified due to seeing the basilisk. Dumbledore got fired and now Harry is trying to enter the Chamber of Secrets. These aren't good news for Lord Voldemort. The problem is, he doesn't want anybody to be able to enter the chamber. The Dark Lord is going to be busy sucking life out of Ginny.</p><p>The Chamber of Secrets is an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> rectangular grid in which some of the cells are columns. A light ray (and a basilisk's gaze) passes through the columns without changing its direction. But with some spell we can make a column magic to reflect the light ray (or the gaze) in all four directions when it receives the ray. This is shown in the figure below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9cfd9e8e43fd3d2588d340d44ee464a2a0be8455.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> The left light ray passes through a regular column, and the right ray — through the magic column. </span> </center><p>The basilisk is located at the right side of the lower right cell of the grid and is looking to the left (in the direction of the lower left cell). According to the legend, anyone who meets a basilisk's gaze directly dies immediately. But if someone meets a basilisk's gaze through a column, this person will get petrified. We know that the door to the Chamber is located on the left side of the upper left corner of the grid and anyone who wants to enter will look in the direction of its movement (in the direction of the upper right cell) from that position.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/331328766492501ef28044eb2346ca44f81d764e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> This figure illustrates the first sample test. </span> </center><p>Given the dimensions of the chamber and the location of regular columns, Lord Voldemort has asked you to find the minimum number of columns that we need to make magic so that anyone who wants to enter the chamber would be petrified or just declare that it's impossible to secure the chamber.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains two integer numbers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i>, <i>m</i> ≤ 1000</span>). Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters. Each character is either \"<span class=\"tex-font-style-tt\">.</span>\" or \"<span class=\"tex-font-style-tt\">#</span>\" and represents one cell of the Chamber grid. It's \"<span class=\"tex-font-style-tt\">.</span>\" if the corresponding cell is empty and \"<span class=\"tex-font-style-tt\">#</span>\" if it's a regular column.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the minimum number of columns to make magic or -1 if it's impossible to do.</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/>.#.<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>4 3<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>The figure above shows the first sample test. In the first sample we should make both columns magic. The dragon figure represents the basilisk and the binoculars represent the person who will enter the Chamber of secrets. The black star shows the place where the person will be petrified. Yellow lines represent basilisk gaze moving through columns.</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=\"07e9bee7541aa5aee3352805a412344d\"/>\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=\"5ffba53baf6e52414710ce740de55eabe4bff8cb\"/>\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/173\">Croc Champ 2012 - Round 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='07e9bee7541aa5aee3352805a412344d'/>\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/173/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=\"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=\"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 *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='07e9bee7541aa5aee3352805a412344d'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1080\"/>\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='07e9bee7541aa5aee3352805a412344d'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1080\"/>\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/4288\" title=\"Croc Champ 2012 — Round 1\" target=\"_blank\">Announcement</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"657:658\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4289\" title=\"Croc Champ 2012 — Round 1 — Editorial\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"659:660\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/173\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/173/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/173/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/173/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/173/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/173/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/173/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/173/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 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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=\"B\" data-uuid=\"ps_8a97b1cf948be7e3965323d843f13ff92bf2f17c\">\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. Chamber of Secrets</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 Chamber of Secrets has been opened again" — this news has spread all around Hogwarts and some of the students have been petrified due to seeing the basilisk. Dumbledore got fired and now Harry is trying to enter the Chamber of Secrets. These aren't good news for Lord Voldemort. The problem is, he doesn't want anybody to be able to enter the chamber. The Dark Lord is going to be busy sucking life out of Ginny.</p><p>The Chamber of Secrets is an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> rectangular grid in which some of the cells are columns. A light ray (and a basilisk's gaze) passes through the columns without changing its direction. But with some spell we can make a column magic to reflect the light ray (or the gaze) in all four directions when it receives the ray. This is shown in the figure below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9cfd9e8e43fd3d2588d340d44ee464a2a0be8455.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> The left light ray passes through a regular column, and the right ray — through the magic column. </span> </center><p>The basilisk is located at the right side of the lower right cell of the grid and is looking to the left (in the direction of the lower left cell). According to the legend, anyone who meets a basilisk's gaze directly dies immediately. But if someone meets a basilisk's gaze through a column, this person will get petrified. We know that the door to the Chamber is located on the left side of the upper left corner of the grid and anyone who wants to enter will look in the direction of its movement (in the direction of the upper right cell) from that position.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/331328766492501ef28044eb2346ca44f81d764e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> This figure illustrates the first sample test. </span> </center><p>Given the dimensions of the chamber and the location of regular columns, Lord Voldemort has asked you to find the minimum number of columns that we need to make magic so that anyone who wants to enter the chamber would be petrified or just declare that it's impossible to secure the chamber.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of the input contains two integer numbers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i>, <i>m</i> ≤ 1000</span>). Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters. Each character is either "<span class=\"tex-font-style-tt\">.</span>" or "<span class=\"tex-font-style-tt\">#</span>" and represents one cell of the Chamber grid. It's "<span class=\"tex-font-style-tt\">.</span>" if the corresponding cell is empty and "<span class=\"tex-font-style-tt\">#</span>" if it's a regular column.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the minimum number of columns to make magic or -1 if it's impossible to do.</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 />.#.<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>4 3<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>The figure above shows the first sample test. In the first sample we should make both columns magic. The dragon figure represents the basilisk and the binoculars represent the person who will enter the Chamber of secrets. The black star shows the place where the person will be petrified. 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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='3300ca74d4382dba1905b54116e2e886'/>\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=\"4303\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4289\"> <p>Croc Champ 2012 — Round 1 — Editorial</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=\"Apr/06/2012 20:51\">12 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>A.</strong> Naive solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> (some simulation all of n rounds) gets TL. Let's speed up this solution. Let's consider rounds on segments [1..mk], [mk+1..2mk], [2mk+1..3mk] and so on. You can see that results of games on these segments will repeat. So you can simulate over exactly one segment and then take into consideration them [n/(mk)] times ([x] is rounding down). Remainder of n%(mk) last rounds you can simulate separately. So you have <span class=\"tex-span\"><i>O</i>(<i>mk</i>)</span> solution that easily fits into time limits.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a> and <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B.</strong> In this problem you should build bipartite graph with n+m vertices. All vertices of the firts part correspond to the rows of the table, vertices of the second part correspond to the columns of the one. Edge connects vertices iff some regular column is placed in the cross of corresponding row and column.</p><p>Firstly death ray covers only last row of the table that corresponds to one of vertices of our graph. When you are changing regular column into magic one, you are allowing death ray "go" by corresponding edge.</p><p>Now you can reformulate the statement by this way: "activate" minimal number of edges in biratrite graph, so some path of minimal lenght connects vertex of the last row of the table and vertex of the first row of the table.</p><p>You can see that required set of edges is just shortest path between these vertices. You can find this path using BFS. If BFS didn't find any path — answer is -1.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>((<i>n</i> + <i>m</i>)<sup class=\"upper-index\">2</sup>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/haas\" title=\"Candidate Master haas\">haas</a>.</p><p><strong>C.</strong> Let's iterate over all spirals and chose one of them that has maximal sum of elements. Because you have <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> spirals, you should calculate sum of any of them in <span class=\"tex-span\"><i>O</i>(1)</span>. Only in this case your solution will fit into time limits.</p><p>Let's define a way for iterate over all spirals. Let's fix one of cells and then iterate over all spirals that have own center in that cell in order of increasing side. So, you can recalculate sum for every spiral from previous one in <span class=\"tex-span\"><i>O</i>(1)</span> using following picture:</p><p><img alt=\" \" src=\"/predownloaded/c6/6c/c66c359162803c71990659a745c7a0c2e9e43683.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>For finding the first "summand", you should in the beginning calculate rectangular partial sums.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>D.</strong> You have bipartite graph with <span class=\"tex-span\">3<i>k</i></span> vertices and should to color its vertices by <span class=\"tex-span\"><i>k</i></span> colors. Every color should be used exactly 3 times and there should be no edges that connect vertices at same color.</p><p>At the first, you should find both of parts of our birartite graph using, for example, DFS. Now let's consider sizes of parts.</p><p>Case 0. If both of sizes divides by 3, you can just split every of parts into groups of 3 vertices and color them.</p><p>Otherwise we can note then size of the first part is 1 modulo 3 and size of the second part is 2 modulo 3.</p><p>There are yet another 2 cases:</p><p>Case 1. You should try to find one vertex from the firts part that have 2 "antiedges" to 2 different vertices of the second part. If you found it, you should color them and reduce the problem to case 0.</p><p>Case 2. There you should try to find 2 vertices on the second part. Every of them should have 2 "antiedges" that "connect" them with 4 different vertices trom the firts part. If you found such 6 vertices, you can color them by 2 different colors and reduce the problem to case 0.</p><p>If you doesn't find coloring using this cases, answer is NO.</p><p>About implementation: it is not clear how to analyse the case 2 in acceptable time. Actually, you can find any two vertices from the second part that have at least two "antiedges". These "antiedges" will conduct to 4 different vertices of the first part because otherwise case 1 would have worked.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span>.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>E.</strong> Let's transform all people into points on a plane with coordinates (<span class=\"tex-span\"><i>x</i> = <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i> = <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>). What the maximal number in group of people that can be formed with some fixed leader? Answer is number of points inside rectangle <span class=\"tex-span\">(<i>x</i>, <i>y</i>): <i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i> ≤ <i>x</i> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>y</i> ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Let's we allready found size of group for every person. How to find maximal group that contain points <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> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>j</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span> both? The required group should have leader with age in range from <span class=\"tex-span\"><i>max</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> - <i>k</i>)</span> то <span class=\"tex-span\"><i>min</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> + <i>k</i>)</span> and responsibility at least <span class=\"tex-span\"><i>max</i>(<i>y</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. From such leaders you should chose one that have maximal size of group. You can see that it is just query for maximum on some rectangle.</p><p>Well, let's learn to quickly find answers for queries of sums in rectangle. You should compress coordinates <span class=\"tex-span\"><i>x</i></span> ans build segment tree for sum. Then you should answer all queries in increasing order of coordinate <span class=\"tex-span\"><i>y</i></span>. When you consider some group with same <span class=\"tex-span\"><i>y</i></span>, you should initially do queries of adding values in points, and after that do sum queries on the segments from <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i></span> to <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i></span>.</p><p>Queries for maximum you can satisfy fully analogicaly using segment tree for maximum.</p><p>So, you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2cd1eac556a7b44fe282c5a5fdd92bc1f8fcd187.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> offline solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</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/173\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 1</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4303\").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: \"4289\",\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=croc\" class=\"tag notice\" style=\"text-decoration: none;\">croc</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012-round-1\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-1</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-4303\"><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'>+103</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4303\"><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=\"Apr/06/2012 20:51\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4289#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/4289#comments\">\n 3\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=\"4313\">\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 (2)</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=\"87322\" 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/P___\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/P___\" title=\"Expert P___\" class=\"rated-user user-blue\">P___</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/07/2012 23:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87322\" href=\"?#comment-87322\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87322\" class=\"CommentVoteFrame\"\r\n class=\"too-negative-comment-vote\"\r\n data-commentRating=\"-48\"\r\n data-commentUserId=\"333\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-48</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87322\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think that this contest was prepared badly. The point weight for task B should be 1500, it could be considered if task C is worth 1500 points too, I would vote for 1000. Because of this fault many coders didn't solve the third problem and waste a lot of time on the second one.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87322 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87322 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87322\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1047416\" 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/tan1shqc\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/tan1shqc\" title=\"Specialist tan1shqc\" class=\"rated-user user-cyan\">tan1shqc</a></div>\n </div>\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/15/2023 09:09\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1047416\" href=\"?#comment-1047416\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1047416\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2729268\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1047416\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>why does this TLE</p><p><a href=\"https://codeforces.com/problemset/submission/173/213861759\">https://codeforces.com/problemset/submission/173/213861759</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1047416 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1047416 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1047416\">\r\n 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Spiral Maximum"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Spiral Maximum</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>Let's consider a <span class=\"tex-span\"><i>k</i> × <i>k</i></span> square, divided into unit squares. Please note that <span class=\"tex-span\"><i>k</i> ≥ 3</span> and is odd. We'll paint squares starting from the upper left square in the following order: first we move to the right, then down, then to the left, then up, then to the right again and so on. We finish moving in some direction in one of two cases: either we've reached the square's border or the square following after the next square is already painted. We finish painting at the moment when we cannot move in any direction and paint a square. The figure that consists of the painted squares is a <span class=\"tex-font-style-it\">spiral</span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/1244f3b40537b25c4b7178c2813c1f58a17d9182.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> The figure shows examples of spirals for <span class=\"tex-span\"><i>k</i> = 3, 5, 7, 9</span>. </span> </center><p>You have an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> table, each of its cells contains a number. Let's consider all possible spirals, formed by the table cells. It means that we consider all spirals of any size that don't go beyond the borders of the table. Let's find the sum of the numbers of the cells that form the spiral. You have to find the maximum of those values among all spirals.</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\">3 ≤ <i>n</i>, <i>m</i> ≤ 500</span>) — the sizes of the table.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> space-separated integers: the <span class=\"tex-span\"><i>j</i></span>-th number in the <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\"> - 1000 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1000</span>) is the number recorded in the <span class=\"tex-span\"><i>j</i></span>-th cell of the <span class=\"tex-span\"><i>i</i></span>-th row of the table.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum sum of numbers among all spirals.</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 5<br/>0 0 0 0 0<br/>1 1 1 1 1<br/>0 0 0 0 1<br/>1 1 1 0 1<br/>1 0 0 0 1<br/>1 1 1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 3<br/>1 1 1<br/>1 0 0<br/>1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 6<br/>-3 2 0 1 5 -1<br/>4 -1 2 -3 0 1<br/>-5 1 2 4 1 -2<br/>0 -2 1 3 -1 2<br/>3 1 4 -3 -2 0<br/>-1 2 -1 3 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>13</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the spiral with maximum sum will cover all 1's of the table.</p><p>In the second sample the spiral may cover only six 1's.</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=\"2fdc6b063148288ef88da1ae99ea2bc2\"/>\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 - 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=\"5ffba53baf6e52414710ce740de55eabe4bff8cb\"/>\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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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. Spiral Maximum</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>Let's consider a <span class=\"tex-span\"><i>k</i> × <i>k</i></span> square, divided into unit squares. Please note that <span class=\"tex-span\"><i>k</i> ≥ 3</span> and is odd. We'll paint squares starting from the upper left square in the following order: first we move to the right, then down, then to the left, then up, then to the right again and so on. We finish moving in some direction in one of two cases: either we've reached the square's border or the square following after the next square is already painted. We finish painting at the moment when we cannot move in any direction and paint a square. The figure that consists of the painted squares is a <span class=\"tex-font-style-it\">spiral</span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/1244f3b40537b25c4b7178c2813c1f58a17d9182.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> The figure shows examples of spirals for <span class=\"tex-span\"><i>k</i> = 3, 5, 7, 9</span>. </span> </center><p>You have an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> table, each of its cells contains a number. Let's consider all possible spirals, formed by the table cells. It means that we consider all spirals of any size that don't go beyond the borders of the table. Let's find the sum of the numbers of the cells that form the spiral. You have to find the maximum of those values among all spirals.</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\">3 ≤ <i>n</i>, <i>m</i> ≤ 500</span>) — the sizes of the table.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> space-separated integers: the <span class=\"tex-span\"><i>j</i></span>-th number in the <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\"> - 1000 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1000</span>) is the number recorded in the <span class=\"tex-span\"><i>j</i></span>-th cell of the <span class=\"tex-span\"><i>i</i></span>-th row of the table.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum sum of numbers among all spirals.</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 5<br />0 0 0 0 0<br />1 1 1 1 1<br />0 0 0 0 1<br />1 1 1 0 1<br />1 0 0 0 1<br />1 1 1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 3<br />1 1 1<br />1 0 0<br />1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 6<br />-3 2 0 1 5 -1<br />4 -1 2 -3 0 1<br />-5 1 2 4 1 -2<br />0 -2 1 3 -1 2<br />3 1 4 -3 -2 0<br />-1 2 -1 3 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>13</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the spiral with maximum sum will cover all 1's of the table.</p><p>In the second sample the spiral may cover only six 1's.</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 $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, 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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=''>13:54:59</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='3300ca74d4382dba1905b54116e2e886'/>\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/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=\"4303\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4289\"> <p>Croc Champ 2012 — Round 1 — Editorial</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=\"Apr/06/2012 20:51\">12 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>A.</strong> Naive solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> (some simulation all of n rounds) gets TL. Let's speed up this solution. Let's consider rounds on segments [1..mk], [mk+1..2mk], [2mk+1..3mk] and so on. You can see that results of games on these segments will repeat. So you can simulate over exactly one segment and then take into consideration them [n/(mk)] times ([x] is rounding down). Remainder of n%(mk) last rounds you can simulate separately. So you have <span class=\"tex-span\"><i>O</i>(<i>mk</i>)</span> solution that easily fits into time limits.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a> and <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B.</strong> In this problem you should build bipartite graph with n+m vertices. All vertices of the firts part correspond to the rows of the table, vertices of the second part correspond to the columns of the one. Edge connects vertices iff some regular column is placed in the cross of corresponding row and column.</p><p>Firstly death ray covers only last row of the table that corresponds to one of vertices of our graph. When you are changing regular column into magic one, you are allowing death ray "go" by corresponding edge.</p><p>Now you can reformulate the statement by this way: "activate" minimal number of edges in biratrite graph, so some path of minimal lenght connects vertex of the last row of the table and vertex of the first row of the table.</p><p>You can see that required set of edges is just shortest path between these vertices. You can find this path using BFS. If BFS didn't find any path — answer is -1.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>((<i>n</i> + <i>m</i>)<sup class=\"upper-index\">2</sup>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/haas\" title=\"Candidate Master haas\">haas</a>.</p><p><strong>C.</strong> Let's iterate over all spirals and chose one of them that has maximal sum of elements. Because you have <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> spirals, you should calculate sum of any of them in <span class=\"tex-span\"><i>O</i>(1)</span>. Only in this case your solution will fit into time limits.</p><p>Let's define a way for iterate over all spirals. Let's fix one of cells and then iterate over all spirals that have own center in that cell in order of increasing side. So, you can recalculate sum for every spiral from previous one in <span class=\"tex-span\"><i>O</i>(1)</span> using following picture:</p><p><img alt=\" \" src=\"/predownloaded/c6/6c/c66c359162803c71990659a745c7a0c2e9e43683.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>For finding the first "summand", you should in the beginning calculate rectangular partial sums.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>D.</strong> You have bipartite graph with <span class=\"tex-span\">3<i>k</i></span> vertices and should to color its vertices by <span class=\"tex-span\"><i>k</i></span> colors. Every color should be used exactly 3 times and there should be no edges that connect vertices at same color.</p><p>At the first, you should find both of parts of our birartite graph using, for example, DFS. Now let's consider sizes of parts.</p><p>Case 0. If both of sizes divides by 3, you can just split every of parts into groups of 3 vertices and color them.</p><p>Otherwise we can note then size of the first part is 1 modulo 3 and size of the second part is 2 modulo 3.</p><p>There are yet another 2 cases:</p><p>Case 1. You should try to find one vertex from the firts part that have 2 "antiedges" to 2 different vertices of the second part. If you found it, you should color them and reduce the problem to case 0.</p><p>Case 2. There you should try to find 2 vertices on the second part. Every of them should have 2 "antiedges" that "connect" them with 4 different vertices trom the firts part. If you found such 6 vertices, you can color them by 2 different colors and reduce the problem to case 0.</p><p>If you doesn't find coloring using this cases, answer is NO.</p><p>About implementation: it is not clear how to analyse the case 2 in acceptable time. Actually, you can find any two vertices from the second part that have at least two "antiedges". These "antiedges" will conduct to 4 different vertices of the first part because otherwise case 1 would have worked.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span>.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>E.</strong> Let's transform all people into points on a plane with coordinates (<span class=\"tex-span\"><i>x</i> = <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i> = <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>). What the maximal number in group of people that can be formed with some fixed leader? Answer is number of points inside rectangle <span class=\"tex-span\">(<i>x</i>, <i>y</i>): <i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i> ≤ <i>x</i> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>y</i> ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Let's we allready found size of group for every person. How to find maximal group that contain points <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> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>j</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span> both? The required group should have leader with age in range from <span class=\"tex-span\"><i>max</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> - <i>k</i>)</span> то <span class=\"tex-span\"><i>min</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> + <i>k</i>)</span> and responsibility at least <span class=\"tex-span\"><i>max</i>(<i>y</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. From such leaders you should chose one that have maximal size of group. You can see that it is just query for maximum on some rectangle.</p><p>Well, let's learn to quickly find answers for queries of sums in rectangle. You should compress coordinates <span class=\"tex-span\"><i>x</i></span> ans build segment tree for sum. Then you should answer all queries in increasing order of coordinate <span class=\"tex-span\"><i>y</i></span>. When you consider some group with same <span class=\"tex-span\"><i>y</i></span>, you should initially do queries of adding values in points, and after that do sum queries on the segments from <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i></span> to <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i></span>.</p><p>Queries for maximum you can satisfy fully analogicaly using segment tree for maximum.</p><p>So, you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2cd1eac556a7b44fe282c5a5fdd92bc1f8fcd187.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> offline solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</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/173\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 1</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4303\").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: \"4289\",\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=croc\" class=\"tag notice\" style=\"text-decoration: none;\">croc</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012-round-1\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-1</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-4303\"><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'>+103</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4303\"><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=\"Apr/06/2012 20:51\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4289#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/4289#comments\">\n 3\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=\"4313\">\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 (2)</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=\"87322\" 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/P___\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/P___\" title=\"Expert P___\" class=\"rated-user user-blue\">P___</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/07/2012 23:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87322\" href=\"?#comment-87322\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87322\" class=\"CommentVoteFrame\"\r\n class=\"too-negative-comment-vote\"\r\n data-commentRating=\"-48\"\r\n data-commentUserId=\"333\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-48</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87322\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think that this contest was prepared badly. The point weight for task B should be 1500, it could be considered if task C is worth 1500 points too, I would vote for 1000. Because of this fault many coders didn't solve the third problem and waste a lot of time on the second one.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87322 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87322 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87322\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1047416\" 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/tan1shqc\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/tan1shqc\" title=\"Specialist tan1shqc\" class=\"rated-user user-cyan\">tan1shqc</a></div>\n </div>\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/15/2023 09:09\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1047416\" href=\"?#comment-1047416\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1047416\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2729268\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1047416\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>why does this TLE</p><p><a href=\"https://codeforces.com/problemset/submission/173/213861759\">https://codeforces.com/problemset/submission/173/213861759</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1047416 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1047416 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1047416\">\r\n 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Deputies"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Deputies</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 Trinitarian kingdom has exactly <span class=\"tex-span\"><i>n</i> = 3<i>k</i></span> cities. All of them are located on the shores of river Trissisipi, which flows through the whole kingdom. Some of the cities are located on one side of the river, and all the rest are on the other side.</p><p>Some cities are connected by bridges built between them. Each bridge connects two cities that are located on the opposite sides of the river. Between any two cities exists no more than one bridge.</p><p>The recently inaugurated King Tristan the Third is busy distributing his deputies among cities. In total there are <span class=\"tex-span\"><i>k</i></span> deputies and the king wants to commission each of them to control exactly three cities. However, no deputy can be entrusted to manage the cities, which are connected by a bridge — the deputy can set a too high fee for travelling over the bridge to benefit his pocket, which is bad for the reputation of the king.</p><p>Help King Tristan the Third distribute the deputies between the cities, if it is 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> — the number of cities and bridges (<span class=\"tex-span\">3 ≤ <i>n</i> < 10<sup class=\"upper-index\">5</sup></span>, <span class=\"tex-span\"><i>n</i> = 3<i>k</i></span>, <span class=\"tex-span\">0 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span>). Next <span class=\"tex-span\"><i>m</i></span> lines describe the bridges. The <span class=\"tex-span\"><i>i</i></span>-th line contains two integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the numbers of cities that are connected by the <span class=\"tex-span\"><i>i</i></span>-th bridge (<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>, <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>i</i> ≤ <i>m</i></span>).</p><p>It is guaranteed that no bridge connects a city with itself and that any two cities are connected with no more than one bridge.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If distributing the deputies in the required manner is impossible, print in a single line \"<span class=\"tex-font-style-tt\">NO</span>\" (without the quotes).</p><p>Otherwise, in the first line print \"<span class=\"tex-font-style-tt\">YES</span>\" (without the quotes), and in the second line print which deputy should be put in charge of each city. The <span class=\"tex-span\"><i>i</i></span>-th number should represent the number of the deputy (from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>), who should be in charge of city numbered <span class=\"tex-span\"><i>i</i></span>-th in the input — overall there should be <span class=\"tex-span\"><i>n</i></span> numbers.</p><p>If there are multiple 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>6 6<br/>1 2<br/>4 1<br/>3 5<br/>6 5<br/>2 6<br/>4 6<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br/>1 2 1 2 2 1 </pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br/>1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO</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=\"a139644cb6ad4f7cb5126b6d29dcc680\"/>\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 - 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=\"5ffba53baf6e52414710ce740de55eabe4bff8cb\"/>\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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Codeforces.setupTutorials(\"/data/problemTutorial\");\n });\n </script>\n\n<script type=\"text/javascript\">\n var _gaq = _gaq || [];\n _gaq.push(['_setAccount', 'UA-743380-5']);\n _gaq.push(['_trackPageview']);\n\n (function () {\n var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;\n ga.src = (document.location.protocol == 'https:' ? 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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/173\">Croc Champ 2012 - Round 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='a139644cb6ad4f7cb5126b6d29dcc680'/>\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/173/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=\"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=\"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=\"Difficulty\">\r\n *2500\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='a139644cb6ad4f7cb5126b6d29dcc680'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1082\"/>\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='a139644cb6ad4f7cb5126b6d29dcc680'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1082\"/>\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/4288\" title=\"Croc Champ 2012 — Round 1\" target=\"_blank\">Announcement</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"657:658\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4289\" title=\"Croc Champ 2012 — Round 1 — Editorial\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"659:660\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/173\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/173/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/173/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/173/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/173/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/173/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/173/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/173/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, 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class=\"header\"><div class=\"title\">D. Deputies</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 Trinitarian kingdom has exactly <span class=\"tex-span\"><i>n</i> = 3<i>k</i></span> cities. All of them are located on the shores of river Trissisipi, which flows through the whole kingdom. Some of the cities are located on one side of the river, and all the rest are on the other side.</p><p>Some cities are connected by bridges built between them. Each bridge connects two cities that are located on the opposite sides of the river. Between any two cities exists no more than one bridge.</p><p>The recently inaugurated King Tristan the Third is busy distributing his deputies among cities. In total there are <span class=\"tex-span\"><i>k</i></span> deputies and the king wants to commission each of them to control exactly three cities. However, no deputy can be entrusted to manage the cities, which are connected by a bridge — the deputy can set a too high fee for travelling over the bridge to benefit his pocket, which is bad for the reputation of the king.</p><p>Help King Tristan the Third distribute the deputies between the cities, if it is 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> — the number of cities and bridges (<span class=\"tex-span\">3 ≤ <i>n</i> < 10<sup class=\"upper-index\">5</sup></span>, <span class=\"tex-span\"><i>n</i> = 3<i>k</i></span>, <span class=\"tex-span\">0 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span>). Next <span class=\"tex-span\"><i>m</i></span> lines describe the bridges. The <span class=\"tex-span\"><i>i</i></span>-th line contains two integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the numbers of cities that are connected by the <span class=\"tex-span\"><i>i</i></span>-th bridge (<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>, <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>i</i> ≤ <i>m</i></span>).</p><p>It is guaranteed that no bridge connects a city with itself and that any two cities are connected with no more than one bridge.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If distributing the deputies in the required manner is impossible, print in a single line "<span class=\"tex-font-style-tt\">NO</span>" (without the quotes).</p><p>Otherwise, in the first line print "<span class=\"tex-font-style-tt\">YES</span>" (without the quotes), and in the second line print which deputy should be put in charge of each city. The <span class=\"tex-span\"><i>i</i></span>-th number should represent the number of the deputy (from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>), who should be in charge of city numbered <span class=\"tex-span\"><i>i</i></span>-th in the input — overall there should be <span class=\"tex-span\"><i>n</i></span> numbers.</p><p>If there are multiple 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>6 6<br />1 2<br />4 1<br />3 5<br />6 5<br />2 6<br />4 6<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br />1 2 1 2 2 1 </pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br />1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO</pre></div></div></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 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=''>13:54:59</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='3300ca74d4382dba1905b54116e2e886'/>\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)\" 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/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=\"4303\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4289\"> <p>Croc Champ 2012 — Round 1 — Editorial</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=\"Apr/06/2012 20:51\">12 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>A.</strong> Naive solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> (some simulation all of n rounds) gets TL. Let's speed up this solution. Let's consider rounds on segments [1..mk], [mk+1..2mk], [2mk+1..3mk] and so on. You can see that results of games on these segments will repeat. So you can simulate over exactly one segment and then take into consideration them [n/(mk)] times ([x] is rounding down). Remainder of n%(mk) last rounds you can simulate separately. So you have <span class=\"tex-span\"><i>O</i>(<i>mk</i>)</span> solution that easily fits into time limits.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a> and <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B.</strong> In this problem you should build bipartite graph with n+m vertices. All vertices of the firts part correspond to the rows of the table, vertices of the second part correspond to the columns of the one. Edge connects vertices iff some regular column is placed in the cross of corresponding row and column.</p><p>Firstly death ray covers only last row of the table that corresponds to one of vertices of our graph. When you are changing regular column into magic one, you are allowing death ray "go" by corresponding edge.</p><p>Now you can reformulate the statement by this way: "activate" minimal number of edges in biratrite graph, so some path of minimal lenght connects vertex of the last row of the table and vertex of the first row of the table.</p><p>You can see that required set of edges is just shortest path between these vertices. You can find this path using BFS. If BFS didn't find any path — answer is -1.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>((<i>n</i> + <i>m</i>)<sup class=\"upper-index\">2</sup>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/haas\" title=\"Candidate Master haas\">haas</a>.</p><p><strong>C.</strong> Let's iterate over all spirals and chose one of them that has maximal sum of elements. Because you have <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> spirals, you should calculate sum of any of them in <span class=\"tex-span\"><i>O</i>(1)</span>. Only in this case your solution will fit into time limits.</p><p>Let's define a way for iterate over all spirals. Let's fix one of cells and then iterate over all spirals that have own center in that cell in order of increasing side. So, you can recalculate sum for every spiral from previous one in <span class=\"tex-span\"><i>O</i>(1)</span> using following picture:</p><p><img alt=\" \" src=\"/predownloaded/c6/6c/c66c359162803c71990659a745c7a0c2e9e43683.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>For finding the first "summand", you should in the beginning calculate rectangular partial sums.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>D.</strong> You have bipartite graph with <span class=\"tex-span\">3<i>k</i></span> vertices and should to color its vertices by <span class=\"tex-span\"><i>k</i></span> colors. Every color should be used exactly 3 times and there should be no edges that connect vertices at same color.</p><p>At the first, you should find both of parts of our birartite graph using, for example, DFS. Now let's consider sizes of parts.</p><p>Case 0. If both of sizes divides by 3, you can just split every of parts into groups of 3 vertices and color them.</p><p>Otherwise we can note then size of the first part is 1 modulo 3 and size of the second part is 2 modulo 3.</p><p>There are yet another 2 cases:</p><p>Case 1. You should try to find one vertex from the firts part that have 2 "antiedges" to 2 different vertices of the second part. If you found it, you should color them and reduce the problem to case 0.</p><p>Case 2. There you should try to find 2 vertices on the second part. Every of them should have 2 "antiedges" that "connect" them with 4 different vertices trom the firts part. If you found such 6 vertices, you can color them by 2 different colors and reduce the problem to case 0.</p><p>If you doesn't find coloring using this cases, answer is NO.</p><p>About implementation: it is not clear how to analyse the case 2 in acceptable time. Actually, you can find any two vertices from the second part that have at least two "antiedges". These "antiedges" will conduct to 4 different vertices of the first part because otherwise case 1 would have worked.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span>.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>E.</strong> Let's transform all people into points on a plane with coordinates (<span class=\"tex-span\"><i>x</i> = <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i> = <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>). What the maximal number in group of people that can be formed with some fixed leader? Answer is number of points inside rectangle <span class=\"tex-span\">(<i>x</i>, <i>y</i>): <i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i> ≤ <i>x</i> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>y</i> ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Let's we allready found size of group for every person. How to find maximal group that contain points <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> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>j</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span> both? The required group should have leader with age in range from <span class=\"tex-span\"><i>max</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> - <i>k</i>)</span> то <span class=\"tex-span\"><i>min</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> + <i>k</i>)</span> and responsibility at least <span class=\"tex-span\"><i>max</i>(<i>y</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. From such leaders you should chose one that have maximal size of group. You can see that it is just query for maximum on some rectangle.</p><p>Well, let's learn to quickly find answers for queries of sums in rectangle. You should compress coordinates <span class=\"tex-span\"><i>x</i></span> ans build segment tree for sum. Then you should answer all queries in increasing order of coordinate <span class=\"tex-span\"><i>y</i></span>. When you consider some group with same <span class=\"tex-span\"><i>y</i></span>, you should initially do queries of adding values in points, and after that do sum queries on the segments from <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i></span> to <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i></span>.</p><p>Queries for maximum you can satisfy fully analogicaly using segment tree for maximum.</p><p>So, you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2cd1eac556a7b44fe282c5a5fdd92bc1f8fcd187.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> offline solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</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/173\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 1</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4303\").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: \"4289\",\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=croc\" class=\"tag notice\" style=\"text-decoration: none;\">croc</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012-round-1\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-1</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-4303\"><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'>+103</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4303\"><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=\"Apr/06/2012 20:51\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4289#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/4289#comments\">\n 3\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=\"4313\">\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 (2)</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=\"87322\" 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/P___\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/P___\" title=\"Expert P___\" class=\"rated-user user-blue\">P___</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/07/2012 23:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87322\" href=\"?#comment-87322\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87322\" class=\"CommentVoteFrame\"\r\n class=\"too-negative-comment-vote\"\r\n data-commentRating=\"-48\"\r\n data-commentUserId=\"333\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-48</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87322\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think that this contest was prepared badly. The point weight for task B should be 1500, it could be considered if task C is worth 1500 points too, I would vote for 1000. Because of this fault many coders didn't solve the third problem and waste a lot of time on the second one.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87322 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87322 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87322\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1047416\" 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/tan1shqc\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/tan1shqc\" title=\"Specialist tan1shqc\" class=\"rated-user user-cyan\">tan1shqc</a></div>\n </div>\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/15/2023 09:09\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1047416\" href=\"?#comment-1047416\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1047416\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2729268\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1047416\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>why does this TLE</p><p><a href=\"https://codeforces.com/problemset/submission/173/213861759\">https://codeforces.com/problemset/submission/173/213861759</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1047416 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1047416 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1047416\">\r\n 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Camping Groups"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Camping Groups</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 club wants to take its members camping. In order to organize the event better the club directors decided to partition the members into several groups. </p><p>Club member <span class=\"tex-span\"><i>i</i></span> has a responsibility value <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> and an age value <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. A <span class=\"tex-font-style-it\">group</span> is a non-empty subset of club members with one member known as group leader. A group leader should be one of the most responsible members of the group (his responsibility value is not less than responsibility of any other group member) and his age absolute difference with any other group member should not exceed <span class=\"tex-span\"><i>k</i></span>. </p><p>Some club members are friends and want to be in the same group. They also like their group to be as large as possible. Now you should write a program that answers a series of questions like \"What's the largest size of a group containing club member <span class=\"tex-span\"><i>x</i></span> and club member <span class=\"tex-span\"><i>y</i></span>?\". It's possible for <span class=\"tex-span\"><i>x</i></span> or <span class=\"tex-span\"><i>y</i></span> to be the group leader.</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\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>, 0 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the number of club members and the age restriction for one group. </p><p>The next line contains integer numbers <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub>, <i>r</i><sub class=\"lower-index\">2</sub>, ..., <i>r</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) separated by space: <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> denotes the <span class=\"tex-span\"><i>i</i></span>-th club member's responsibility. In the same way there are integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></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>) in the third line: <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> denotes the <span class=\"tex-span\"><i>i</i></span>-th club member's age.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> denoting the number of questions that you should answer (<span class=\"tex-span\">1 ≤ <i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span>). The next <span class=\"tex-span\"><i>q</i></span> lines describe the questions. Each line contains 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\">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>, <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the indices of the club members that should end up in the same group. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each question print the maximum size of the group in a line. If making such a group is impossible print -1 instead.</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 1<br/>1 5 4 1 2<br/>4 4 3 2 2<br/>4<br/>5 3<br/>2 3<br/>2 5<br/>4 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br/>3<br/>-1<br/>4<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first query the largest group with members 3 and 5 is <span class=\"tex-span\">{1, 3, 4, 5}</span> where member 3 is the leader.</p><p>In the second query member 2 should be the leader so the group will be <span class=\"tex-span\">{1, 2, 3}</span>.</p><p>In the third query the leader of the group should have age 3 so the only leader can be member 3, who is less responsible than member 2. So making a group is impossible.</p><p>The group for the fourth query is the same as first query.</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=\"8befb7618389c09308d59d781eb97412\"/>\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=\"5ffba53baf6e52414710ce740de55eabe4bff8cb\"/>\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/173\">Croc Champ 2012 - Round 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='8befb7618389c09308d59d781eb97412'/>\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/173/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=\"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=\"Difficulty\">\r\n *2600\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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|| 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_31a372c920815d1d0430e8166d17d82b641745ba\">\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. Camping Groups</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 club wants to take its members camping. In order to organize the event better the club directors decided to partition the members into several groups. </p><p>Club member <span class=\"tex-span\"><i>i</i></span> has a responsibility value <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> and an age value <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. A <span class=\"tex-font-style-it\">group</span> is a non-empty subset of club members with one member known as group leader. A group leader should be one of the most responsible members of the group (his responsibility value is not less than responsibility of any other group member) and his age absolute difference with any other group member should not exceed <span class=\"tex-span\"><i>k</i></span>. </p><p>Some club members are friends and want to be in the same group. They also like their group to be as large as possible. Now you should write a program that answers a series of questions like "What's the largest size of a group containing club member <span class=\"tex-span\"><i>x</i></span> and club member <span class=\"tex-span\"><i>y</i></span>?". It's possible for <span class=\"tex-span\"><i>x</i></span> or <span class=\"tex-span\"><i>y</i></span> to be the group leader.</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\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>, 0 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the number of club members and the age restriction for one group. </p><p>The next line contains integer numbers <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub>, <i>r</i><sub class=\"lower-index\">2</sub>, ..., <i>r</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) separated by space: <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> denotes the <span class=\"tex-span\"><i>i</i></span>-th club member's responsibility. In the same way there are integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></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>) in the third line: <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> denotes the <span class=\"tex-span\"><i>i</i></span>-th club member's age.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> denoting the number of questions that you should answer (<span class=\"tex-span\">1 ≤ <i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span>). The next <span class=\"tex-span\"><i>q</i></span> lines describe the questions. Each line contains 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\">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>, <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the indices of the club members that should end up in the same group. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each question print the maximum size of the group in a line. If making such a group is impossible print -1 instead.</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 1<br />1 5 4 1 2<br />4 4 3 2 2<br />4<br />5 3<br />2 3<br />2 5<br />4 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br />3<br />-1<br />4<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first query the largest group with members 3 and 5 is <span class=\"tex-span\">{1, 3, 4, 5}</span> where member 3 is the leader.</p><p>In the second query member 2 should be the leader so the group will be <span class=\"tex-span\">{1, 2, 3}</span>.</p><p>In the third query the leader of the group should have age 3 so the only leader can be member 3, who is less responsible than member 2. 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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='3300ca74d4382dba1905b54116e2e886'/>\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 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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=\"4303\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4289\"> <p>Croc Champ 2012 — Round 1 — Editorial</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=\"Apr/06/2012 20:51\">12 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>A.</strong> Naive solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> (some simulation all of n rounds) gets TL. Let's speed up this solution. Let's consider rounds on segments [1..mk], [mk+1..2mk], [2mk+1..3mk] and so on. You can see that results of games on these segments will repeat. So you can simulate over exactly one segment and then take into consideration them [n/(mk)] times ([x] is rounding down). Remainder of n%(mk) last rounds you can simulate separately. So you have <span class=\"tex-span\"><i>O</i>(<i>mk</i>)</span> solution that easily fits into time limits.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a> and <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B.</strong> In this problem you should build bipartite graph with n+m vertices. All vertices of the firts part correspond to the rows of the table, vertices of the second part correspond to the columns of the one. Edge connects vertices iff some regular column is placed in the cross of corresponding row and column.</p><p>Firstly death ray covers only last row of the table that corresponds to one of vertices of our graph. When you are changing regular column into magic one, you are allowing death ray "go" by corresponding edge.</p><p>Now you can reformulate the statement by this way: "activate" minimal number of edges in biratrite graph, so some path of minimal lenght connects vertex of the last row of the table and vertex of the first row of the table.</p><p>You can see that required set of edges is just shortest path between these vertices. You can find this path using BFS. If BFS didn't find any path — answer is -1.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>((<i>n</i> + <i>m</i>)<sup class=\"upper-index\">2</sup>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/haas\" title=\"Candidate Master haas\">haas</a>.</p><p><strong>C.</strong> Let's iterate over all spirals and chose one of them that has maximal sum of elements. Because you have <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> spirals, you should calculate sum of any of them in <span class=\"tex-span\"><i>O</i>(1)</span>. Only in this case your solution will fit into time limits.</p><p>Let's define a way for iterate over all spirals. Let's fix one of cells and then iterate over all spirals that have own center in that cell in order of increasing side. So, you can recalculate sum for every spiral from previous one in <span class=\"tex-span\"><i>O</i>(1)</span> using following picture:</p><p><img alt=\" \" src=\"/predownloaded/c6/6c/c66c359162803c71990659a745c7a0c2e9e43683.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>For finding the first "summand", you should in the beginning calculate rectangular partial sums.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>D.</strong> You have bipartite graph with <span class=\"tex-span\">3<i>k</i></span> vertices and should to color its vertices by <span class=\"tex-span\"><i>k</i></span> colors. Every color should be used exactly 3 times and there should be no edges that connect vertices at same color.</p><p>At the first, you should find both of parts of our birartite graph using, for example, DFS. Now let's consider sizes of parts.</p><p>Case 0. If both of sizes divides by 3, you can just split every of parts into groups of 3 vertices and color them.</p><p>Otherwise we can note then size of the first part is 1 modulo 3 and size of the second part is 2 modulo 3.</p><p>There are yet another 2 cases:</p><p>Case 1. You should try to find one vertex from the firts part that have 2 "antiedges" to 2 different vertices of the second part. If you found it, you should color them and reduce the problem to case 0.</p><p>Case 2. There you should try to find 2 vertices on the second part. Every of them should have 2 "antiedges" that "connect" them with 4 different vertices trom the firts part. If you found such 6 vertices, you can color them by 2 different colors and reduce the problem to case 0.</p><p>If you doesn't find coloring using this cases, answer is NO.</p><p>About implementation: it is not clear how to analyse the case 2 in acceptable time. Actually, you can find any two vertices from the second part that have at least two "antiedges". These "antiedges" will conduct to 4 different vertices of the first part because otherwise case 1 would have worked.</p><p>This solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span>.</p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Ripatti\" title=\"Master Ripatti\">Ripatti</a>.</p><p><strong>E.</strong> Let's transform all people into points on a plane with coordinates (<span class=\"tex-span\"><i>x</i> = <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i> = <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>). What the maximal number in group of people that can be formed with some fixed leader? Answer is number of points inside rectangle <span class=\"tex-span\">(<i>x</i>, <i>y</i>): <i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i> ≤ <i>x</i> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>y</i> ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Let's we allready found size of group for every person. How to find maximal group that contain points <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> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>j</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span> both? The required group should have leader with age in range from <span class=\"tex-span\"><i>max</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> - <i>k</i>)</span> то <span class=\"tex-span\"><i>min</i>(<i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i>, <i>x</i><sub class=\"lower-index\"><i>j</i></sub> + <i>k</i>)</span> and responsibility at least <span class=\"tex-span\"><i>max</i>(<i>y</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. From such leaders you should chose one that have maximal size of group. You can see that it is just query for maximum on some rectangle.</p><p>Well, let's learn to quickly find answers for queries of sums in rectangle. You should compress coordinates <span class=\"tex-span\"><i>x</i></span> ans build segment tree for sum. Then you should answer all queries in increasing order of coordinate <span class=\"tex-span\"><i>y</i></span>. When you consider some group with same <span class=\"tex-span\"><i>y</i></span>, you should initially do queries of adding values in points, and after that do sum queries on the segments from <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> - <i>k</i></span> to <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> + <i>k</i></span>.</p><p>Queries for maximum you can satisfy fully analogicaly using segment tree for maximum.</p><p>So, you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2cd1eac556a7b44fe282c5a5fdd92bc1f8fcd187.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> offline solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</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/173\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 1</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4303\").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: \"4289\",\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=croc\" class=\"tag notice\" style=\"text-decoration: none;\">croc</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012-round-1\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-1</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-4303\"><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'>+103</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4303\"><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=\"Apr/06/2012 20:51\">12 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4289#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/4289#comments\">\n 3\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=\"4313\">\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 (2)</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=\"87322\" 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/P___\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/P___\" title=\"Expert P___\" class=\"rated-user user-blue\">P___</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/07/2012 23:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87322\" href=\"?#comment-87322\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87322\" class=\"CommentVoteFrame\"\r\n class=\"too-negative-comment-vote\"\r\n data-commentRating=\"-48\"\r\n data-commentUserId=\"333\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-48</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87322\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think that this contest was prepared badly. The point weight for task B should be 1500, it could be considered if task C is worth 1500 points too, I would vote for 1000. Because of this fault many coders didn't solve the third problem and waste a lot of time on the second one.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87322 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87322 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87322\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1047416\" 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/tan1shqc\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/tan1shqc\" title=\"Specialist tan1shqc\" class=\"rated-user user-cyan\">tan1shqc</a></div>\n </div>\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/15/2023 09:09\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1047416\" href=\"?#comment-1047416\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1047416\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2729268\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1047416\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>why does this TLE</p><p><a href=\"https://codeforces.com/problemset/submission/173/213861759\">https://codeforces.com/problemset/submission/173/213861759</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1047416 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1047416 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1047416\">\r\n 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Problem About Equation"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Problem About Equation</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 group of <span class=\"tex-span\"><i>n</i></span> merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the <span class=\"tex-span\"><i>n</i></span> mugs must be the same.</p><p>Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> milliliters of the drink, the second one has <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span> milliliters and so on. The bottle has <span class=\"tex-span\"><i>b</i></span> milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.</p><p>Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously: </p><ul> <li> there were <span class=\"tex-span\"><i>b</i></span> milliliters poured in total. That is, the bottle need to be emptied; </li><li> after the process is over, the volumes of the drink in the mugs should be equal. </li></ul></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a pair of integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>b</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 100, 1 ≤ <i>b</i> ≤ 100</span>), where <span class=\"tex-span\"><i>n</i></span> is the total number of friends in the group and <span class=\"tex-span\"><i>b</i></span> is the current volume of drink in the bottle. The second line contains a sequence of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span>), where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the current volume of drink in the <span class=\"tex-span\"><i>i</i></span>-th mug.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number \"<span class=\"tex-font-style-tt\">-1</span>\" (without the quotes), if there is no solution. Otherwise, print <span class=\"tex-span\"><i>n</i></span> float numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, <i>c</i><sub class=\"lower-index\">2</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>n</i></sub></span>, where <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> is the volume of the drink to add in the <span class=\"tex-span\"><i>i</i></span>-th mug. Print the numbers with no less than 6 digits after the decimal point, print each <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> on a single line. Polycarpus proved that if a solution exists then it is unique.</p><p>Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma.</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 50<br/>1 2 3 4 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>12.000000<br/>11.000000<br/>10.000000<br/>9.000000<br/>8.000000<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2<br/>1 100<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=\"3c23083273a4b396894c4a81582326ee\"/>\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=\"e25a2e8453e479693c0806119fdba17b9f05c3f0\"/>\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=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4302\" title=\"VK Cup 2012 Round 3\" target=\"_blank\">VK Cup 2012 Round 3</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"661:662\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4303\" title=\"VK Cup 2012 Round 3 — Разбор\" 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=\"663\" resourceName=\"VK Cup 2012 Round 3 — Разбор\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: 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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_f407935d11f11f9f4ad58c390d7d53a5bfa18ad7\">\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. Problem About Equation</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 group of <span class=\"tex-span\"><i>n</i></span> merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the <span class=\"tex-span\"><i>n</i></span> mugs must be the same.</p><p>Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> milliliters of the drink, the second one has <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span> milliliters and so on. The bottle has <span class=\"tex-span\"><i>b</i></span> milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.</p><p>Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously: </p><ul> <li> there were <span class=\"tex-span\"><i>b</i></span> milliliters poured in total. That is, the bottle need to be emptied; </li><li> after the process is over, the volumes of the drink in the mugs should be equal. </li></ul></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a pair of integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>b</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 100, 1 ≤ <i>b</i> ≤ 100</span>), where <span class=\"tex-span\"><i>n</i></span> is the total number of friends in the group and <span class=\"tex-span\"><i>b</i></span> is the current volume of drink in the bottle. The second line contains a sequence of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span>), where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the current volume of drink in the <span class=\"tex-span\"><i>i</i></span>-th mug.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number "<span class=\"tex-font-style-tt\">-1</span>" (without the quotes), if there is no solution. Otherwise, print <span class=\"tex-span\"><i>n</i></span> float numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, <i>c</i><sub class=\"lower-index\">2</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>n</i></sub></span>, where <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> is the volume of the drink to add in the <span class=\"tex-span\"><i>i</i></span>-th mug. Print the numbers with no less than 6 digits after the decimal point, print each <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> on a single line. Polycarpus proved that if a solution exists then it is unique.</p><p>Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma.</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 50<br />1 2 3 4 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>12.000000<br />11.000000<br />10.000000<br />9.000000<br />8.000000<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2<br />1 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-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=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=''>13:55:07</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='f8539b4f84c368e0f04723c04d0da3b3'/>\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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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/Burunduk1\">Burunduk1</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Burunduk1\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Burunduk1\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Burunduk1\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Burunduk1\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Burunduk1\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Burunduk1\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Burunduk1\" style=\"text-decoration:none;color:black !important;\">Burunduk1'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=\"4317\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4303\"> <p>VK Cup 2012 Round 3 — Разбор</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a>,\r\n <span class=\"format-humantime\" title=\"Apr/08/2012 22:13\">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><a href=\"/contest/164/problem/A\" title=\"VK Cup 2012 Раунд 3\">164A - Переменная, или Туда и обратно</a></p><p><strong>Кратко о решении — dfs, O(E).</strong></p><p>Пустим поиск в глубину из всех вершин, где переменная присваивается. Пометим все посещенные.</p><p>Пустим поиск в глубину по обратным ребрам из всех вершин, где переменная используется. Запретим ему проходить по вершинам, где переменная присваивается. Пометим все посещенные.</p><p>Вершины помеченные оба раза — это и есть те вершины, где состояние Васи кого-то волнует</p><p><a href=\"/contest/164/problem/B\" title=\"VK Cup 2012 Раунд 3\">164B - Древние берляндские иероглифы</a></p><p><strong>Кратко о решении — метод двух указателей, O(N).</strong></p><p>Давайте для удобства предположим, что каждый символ в каждой строке встречается ровно один раз.</p><p>Тогда у нас есть перестановка <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (позиция во второй строке <span class=\"tex-span\"><i>i</i></span>-го символа первой строки)</p><p>Решение за квадрат теперь такое: фиксируем начало подстроки и идем по ней вперед, при этом параллельно идем по подпоследовательности и следим, что и там, и там мы не прошли больше круга.</p><p>Решение за линию.</p><p>Будем теперь идти двумя указателями "начало подстроки" и "конец подстроки". Параллельно будем хранить очередь — текущая парная подпоследовательность. В очереди все <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> обязательно возрастают (этого не сложно достичь, т.к. можно прибавлять к <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> число <span class=\"tex-span\"><i>n</i></span> столько раз, сколько нужно. То что подпоследовательность не зациклилась проверяется так <span class=\"tex-span\"><i>queue</i>.<i>first</i> - <i>queue</i>.<i>last</i> < <i>n</i></span>. Значит, мы можем двигать конец подстроки вперед, пока это неравенство выполнено. Как только конец подстроки нельзя увеличить, увеличиваем начало. Заметим, что начало и конец подстроки также двигаются по кругу.</p><p>Альтернативное решение:</p><p>После того, как мы увидели перестановку <span class=\"tex-span\"><i>p</i></span>, можно воспользоваться методом двоичных подъемов и получить решение за O(NlogN), которое тоже получало Accepted.</p><p><a href=\"/contest/164/problem/C\" title=\"VK Cup 2012 Раунд 3\">164C - Автоматное программирование</a></p><p><strong>Кратко о решении — MinCost flow, O(<span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> K) или O(NlogN K).</strong></p><p>Самое главное было — увидеть граф, где вершины = задания, множества заданий, выполняемые автоматами = вершиннонепересекающиеся пути, а ребра можно было строить двумя способами (см. ниже).</p><p>Как сделать пути вершиннонепересекающимися? Раздвоить вершины.</p><p>Как добавить стоимость? Между двумя половинками вершины должна быть стоимость <span class=\"tex-span\"> - <i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Первый способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> : вершины A, B соединены ребром, если после задания A можно успеть выполнить задание B тем же автоматом. Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Второй способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">2</sub></span> : все вершины упорядочены по <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> из вершины i ведут два ребра — в <span class=\"tex-span\"><i>i</i> + 1</span> (не берем <span class=\"tex-span\"><i>i</i></span> задание, пробуем взять следующее) и в вершину с минимальным <span class=\"tex-span\"><i>j</i></span> : <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub> ≥ <i>s</i><sub class=\"lower-index\"><i>i</i></sub> + <i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (берем задание, переходим к минимальному из возможных следующих). Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span>.</p><p>Если вы пользовались первым способом и для поиска пути реализовали одну из вариаций алгоритма Форда-Беллмана, то вы могли получить TL. Собственно пока из-за того, что на java все медленно, TL не подняли, все Форд-Беллманы кроме одного особенного получали заслуженный TL.</p><p>Чтобы в <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> использовать Дейкстру с потенциалами, удобнее всего было заметить, что граф ацикличен и первый раз расстояния посчитать за O(E).</p><p><a href=\"/contest/164/problem/D\" title=\"VK Cup 2012 Раунд 3\">164D - Минимальный диаметр</a></p><p><strong>Кратко о решении — бинпоиск по ответу, а внутри перебор за O(Fib(K)).</strong></p><p>Правильное решение состояло из четырех несложных идей:</p><p>1) Нужно из <span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> ребер покрыть удаленными вершинами сколько то максимальных. Когда мы покрываем еще не покрытое ребро, у нас 2 варианта это сделать — выбрать 1 конец, выбрать второй конец. Эта идея сама по себе давала асимптотику <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>K</i></sup> * <i>N</i>)</span>.</p><p>2) Если сделать бинпоиск по ответу, то мы решаем более простую задачу: можно ли покрыть первые X ребер K вершинами? Т.е. правда ли, что размер контролирующего множества в таком графе не более K. </p><p>3) Если мы теперь внутри бинпоиска не берем какую-то вершину, то мы должны брать всех ее соседей в уменьшенном графе. Из этого можно сделать 2 вывода: во-первых, если есть вершина степени больше чем K, ее брать обязательно, во-вторых, не выгодно брать вершину степени 1.</p><p>4) Теперь решение работает за log * Fib(K) * K, где log — константа от бинпоиска, Fib(K) — K-е число Фибоначчи, K --- максимальная степень вершины в уменьшенном графе.</p><p>Почему Fib(K)? Теперь, когда мы делаем выбор, в одной ветке рекурсии K уменьшается на 1, а в другой хотя бы на 2... На лицо числа Фибоначчи.</p><p>P.S. Из похожих задач я знаю вот эту: <a href=\"http://neerc.ifmo.ru/school/archive/2009-2010/ru-olymp-roi-2010-statements.rar\">задача 2 с РОИ 2009-2010</a></p><p><a href=\"/contest/164/problem/E\" title=\"VK Cup 2012 Раунд 3\">164E - Поликарп и работы</a></p><p><strong>Кратко о решении — жадность + куча запросов на отрезке, асимптотика = O(NlogN).</strong></p><p>В этой задаче так и не получилось написать очевидное условие...</p><p>Расскажу некоторую легенду, чтобы дать понять, что задачка не искусственна, взята из "реальной жизни".</p><p>Все вы читали задачу C. Давайте чуть поменяем ее, скажем, что автомат у нас один, а работа должна начаться не раньше <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, закончиться на позже <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, а времени на нее уйдет <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Рассмотрим случай, когда <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> возрастают.</p><p>Попробуем придумать жадное решение: отсортируем все работы по <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и будем пытаться "брать". Если можно взять, то выполнять работу будем в минимально возможный момент времени.</p><p>Это жадное решение не сложно завалить тестом (L=1, R=10, T=10), (L=2,R=11,T=5), (L=3,R=12,T=5).</p><p>Поэтому давайте жадность улучшим, попробуем, если добавить в конец не получается менять на кого-нибудь так, чтобы правый конец (последний использованный момент времени) максимально уменьшился.</p><p>Собственно задача E состояла в моделировании процесса. В том, чтобы запрограммировать эту жадность.</p><p><strong>Итак, решение:</strong></p><p>Для каждого отрезка определим величину <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>i</i></sub></span> = <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> — <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> (насколько можно отрезок подвинуть влево).</p><p>У нас уже есть <span class=\"tex-span\"><i>k</i></span> отрезков. Добавляем <span class=\"tex-span\"><i>k</i> + 1</span>-й, не получается. Пробуем сделать замену. Перебираем все отрезки в порядке уменьшения индекса, смотрим, насколько уменьшится правый конец.</p><p>Это min(<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>, min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Т.е. ни один из отрезков из 1..i уже не даст ответ лучше, чем min(max по j=i+1..k (<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>), min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Зачем я выдумал этот максимум? Дело в том, что под минимумом теперь две функции, убывающая и возрастающая. Значит, максимум можно искать бинарным или троичным поиском.</p><p>Следующая идея заключается в том, что когда мы нашли оптимальную замену <span class=\"tex-span\"><i>besti</i></span>, то чтобы пересчитать все <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>, достаточно сделать вычитание на отрезке besti+1..k</p><p>Полученное решение имеет асимптотику <span class=\"tex-span\"><i>O</i>(<i>Nlog</i><sup class=\"upper-index\">2</sup><i>N</i>)</span>. Его можно улучшить до <span class=\"tex-span\"><i>O</i>(<i>NlogN</i>)</span>, заменив бинпоиск, а внутри него обращение к дереву поиска или дереву отрезков на один спуск по дереву.</p><p><strong>UPD:</strong></p><p><strong>По просьбам участников выкладываю "разбор" задач A,B,C второго дивизиона.</strong></p><p>Задачи второго дивизиона я не готовил, не читал, не решал. Но вроде бы, если почитать, они решаются так, как описано ниже. Так что разбор второго дивизиона не стоит воспринимать как авторский, это просто рассказ "как бы я решал эти задачки". Надеюсь, нигде не наврал.</p><p><a href=\"https://codeforces.com/contest/174/problem/A\">Задача A</a></p><p>X = (<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></span> + b) / n.</p><p>Если <span class=\"tex-span\"><i>X</i></span> <strong>меньше</strong> максимального <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нельзя сделать так, как просят. Иначе нужно вывести числа X — <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/B\">Задача B</a></p><p><strong>Решение #1, жадное:</strong> </p><p>Если между двумя точками больше 11 или меньше 2 символов, то нельзя так разрезать.</p><p>Если перед первой точкой больше 8 символов, то нельзя так разрезать.</p><p>Если между после последней точки больше 3 символов, то нельзя так разрезать.</p><p>А иначе режем жадно :-) Если количество символов между двумя точками равно X, то разрез проводится в позиции min(8,X-1).</p><p><strong>Решение #2, DP:</strong> </p><p>is[i] — можем ли мы разрезать префикс длины <span class=\"tex-span\"><i>i</i></span>.</p><p>Изначально is[0] = 1, остальные нули.</p><p>Теперь перебираем <span class=\"tex-span\"><i>i</i></span> в порядке возрастания и если is[i] = 1, пытаемся сделать переход в <span class=\"tex-span\"><i>i</i> + 1</span>..<span class=\"tex-span\"><i>i</i> + 12</span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/C\">Задача C</a></p><p>Основная идея — жадность.</p><p>Если минимум на всем массиве равен нулю, то задача естественным образом распадается на подзадачи, а иначе нужно уменьшить весь отрезок на 1.</p><p><strong>Решение #1, ищем минимум</strong></p><p>Ищем минимум в массиве, вычитаем 1 из всего массива <span class=\"tex-span\"><i>min</i></span> раз, задача распадается на несколько (т.е. в каждый момент времени, задача = отрезок исходного массива). Минимум на отрезке нужно искать быстро, за O(logN), например.</p><p><strong>Решение #2, простое</strong></p><p>Будем идти слева направо и хранить, сколько у нас отрезков уже начато торчит налево, пусть это X. Если <span class=\"tex-span\"><i>X</i> < <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нужно начать несколько новых отрезков, если же <span class=\"tex-span\"><i>X</i> > <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то несколько уже начатых нужно закончить в позиции <span class=\"tex-span\"><i>i</i> - 1</span>. Начатые отрезки можно хранить в стэке. Хранить, конечно, нужно только позицию начала. Новый <span class=\"tex-span\"><i>X</i></span> будет равен <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><strong>Конец.</strong></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-148-4317\").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: \"148\",\n blogEntryId: \"4303\",\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=vkcup2012\" class=\"tag notice\" style=\"text-decoration: none;\">vkcup2012</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round3\" class=\"tag notice\" style=\"text-decoration: none;\">round3</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=%D1%80%D0%B0%D0%B7%D0%B1%D0%BE%D1%80\" class=\"tag notice\" style=\"text-decoration: none;\">разбор</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-4317\"><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'>+70</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4317\"><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/Burunduk1\"><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/Burunduk1\">\n Burunduk1\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=\"Apr/08/2012 22:13\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4303#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/4303#comments\">\n 9\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=\"4327\">\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 (8)</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=\"87633\" 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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87633\" href=\"?#comment-87633\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87633\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87633\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for writing up this. Can we expect an English version? </p><p>With Google translate, 164D's method is showed as "binpoisk to answer", what does "binpoisk" mean? Is it same as binary search?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87633 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87633 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87633\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87634\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/andreyv\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5720/avatar/26e7479dac2e8287.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/andreyv\" title=\"Expert andreyv\" class=\"rated-user user-blue\">andreyv</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87634\" href=\"?#comment-87634\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87634\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"5720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87634\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, it's an abbreviation of the two words.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87634 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87634 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87634\">\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=\"87658\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Burunduk1\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/347/avatar/8e55ad6d55eef9fa.jpg'/> </a>\n <div><a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 06:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87658\" href=\"?#comment-87658\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87658\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"347\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87658\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes. Binary Search = Binarniy Poisk = Binpoisk.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87658 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87658 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87658\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87674\" commentParentId=\"87658\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 20:26\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87674\" href=\"?#comment-87674\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87658\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87674\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87674\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks to both of you.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87674 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87674 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87674\">\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=\"541075\" 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/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/06/2019 13:44\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541075\" href=\"?#comment-541075\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541075\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541075\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Could anyone tell me a detailed explanation about dp approach for problem B. I'am learning DP.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541075 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541075 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541075\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"541309\" commentParentId=\"541075\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/07/2019 16:05\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541309\" href=\"?#comment-541309\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-541075\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541309\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541309\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/174/submission/60219361\">My solution</a> for problem B using DP approach!!! </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541309 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541309 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541309\">\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=\"591779\" 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/kesh4281\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/kesh4281\" title=\"Candidate Master kesh4281\" class=\"rated-user user-violet\">kesh4281</a></div>\n </div>\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/23/2020 13:18\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-591779\" href=\"?#comment-591779\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"591779\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"851343\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-591779\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Problem C, there are some good comments in announcement section as well. start=si finish=si+ti so times which are important are starts and finishes only. First coordinate compress all the times (starts and finishes) now let we have times like t1 t2 t3... t2n (at max we can have 2*n times) Let there be x distinct time. now connect vertices ti to ti+1 for all 1<=i<=x-1 with capacity k, cost 0 connect vertices ta to tb if we have a task that started at ta and ends at tb-1 (Read question carefully, a task starts at si and finishes at si+ti-1, and at si+ti machine is free). Capacity=1, Cost= -Cost of edge.</p><p>Now it becomes mincost maxflow problem with max flow upto k. If u didnt get it then just above graph once for sample input. u will surely understand.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-591779 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-591779 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-591779\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1039946\" 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/nonrice\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2487084/avatar/f9f0266eade11795.jpg'/> </a>\n <div><a href=\"/profile/nonrice\" title=\"Expert nonrice\" class=\"rated-user user-blue\">nonrice</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/22/2023 19:35\">4 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1039946\" href=\"?#comment-1039946\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1039946\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2487084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1039946\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did reverse version (maximum to minimum) way in C-Range Increments using dsu</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1039946 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1039946 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1039946\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4327\" 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</div>\n <script type=\"application/javascript\">\n $(function() {\n $(\".userListMarker\").click(function() {\n $.post(\"/data/lists\", {action: \"findTouched\"}, function(json) {\n Codeforces.facebox(\".userListsFacebox\");\n var tbody = $(\"#facebox tbody\");\n tbody.empty();\n for (var i in json) {\n tbody.append(\n $(\"<tr></tr>\").append(\n $(\"<td></td>\").attr(\"data-readKey\", json[i].readKey).text(json[i].name)\n )\n );\n }\n Codeforces.updateDatatables();\n tbody.find(\"td\").css(\"cursor\", \"pointer\").click(function() {\n document.location = Codeforces.updateUrlParameter(document.location.href, \"list\", $(this).attr(\"data-readKey\"));\n });\n }, \"json\");\n });\n });\n </script>\n</div>\n <script type=\"application/javascript\">\n if ('serviceWorker' in navigator && 'fetch' in window && 'caches' in window) {\n navigator.serviceWorker.register('/service-worker-81027.js')\n .then(function (registration) {\n console.log('Service worker registered: ', registration);\n })\n .catch(function (error) {\n console.log('Registration failed: ', error);\n });\n }\n </script>\n<script>(function(){var js = \"window['__CF$cv$params']={r:'812870ec2b914991',t:'MTY5NjcwNTc5NC4xMDkwMDA='};_cpo=document.createElement('script');_cpo.nonce='',_cpo.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js',document.getElementsByTagName('head')[0].appendChild(_cpo);\";var _0xh = document.createElement('iframe');_0xh.height = 1;_0xh.width = 1;_0xh.style.position = 'absolute';_0xh.style.top = 0;_0xh.style.left = 0;_0xh.style.border = 'none';_0xh.style.visibility = 'hidden';document.body.appendChild(_0xh);function handler() {var _0xi = _0xh.contentDocument || _0xh.contentWindow.document;if (_0xi) {var _0xj = _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":852,"cells":{"problem_id":{"kind":"string","value":"174B"},"contest":{"kind":"string","value":"174"},"problem":{"kind":"string","value":"B"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B. File List"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. File List</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>Eudokimus, a system administrator is in trouble again. As a result of an error in some script, a list of names of very important files has been damaged. Since they were files in the BerFS file system, it is known that each file name has a form \"<span class=\"tex-font-style-tt\">name.ext</span>\", where: </p><ul> <li> <span class=\"tex-font-style-tt\">name</span> is a string consisting of lowercase Latin letters, its length is from 1 to 8 characters; </li><li> <span class=\"tex-font-style-tt\">ext</span> is a string consisting of lowercase Latin letters, its length is from 1 to 3 characters. </li></ul><p>For example, \"<span class=\"tex-font-style-tt\">read.me</span>\", \"<span class=\"tex-font-style-tt\">example.txt</span>\" and \"<span class=\"tex-font-style-tt\">b.cpp</span>\" are valid file names and \"<span class=\"tex-font-style-tt\">version.info</span>\", \"<span class=\"tex-font-style-tt\">ntldr</span>\" and \"<span class=\"tex-font-style-tt\">contestdata.zip</span>\" are not.</p><p>Damage to the list meant that all the file names were recorded one after another, without any separators. So now Eudokimus has a single string.</p><p>Eudokimus needs to set everything right as soon as possible. He should divide the resulting string into parts so that each part would be a valid file name in BerFS. Since Eudokimus has already proved that he is not good at programming, help him. The resulting file list can contain the same file names.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input data consists of a single string <span class=\"tex-span\"><i>s</i></span>, its length is from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">4·10<sup class=\"upper-index\">5</sup></span> characters. The string can contain only lowercase Latin letters ('<span class=\"tex-font-style-tt\">a</span>' - '<span class=\"tex-font-style-tt\">z</span>') and periods ('<span class=\"tex-font-style-tt\">.</span>').</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print \"<span class=\"tex-font-style-tt\">YES</span>\" (without the quotes), if it is possible to divide <span class=\"tex-span\"><i>s</i></span> into parts as required. In this case, the following lines should contain the parts of the required partition, one per line in the order in which they appear in <span class=\"tex-span\"><i>s</i></span>. The required partition can contain the same file names. If there are multiple solutions, print any of them.</p><p>If the solution does not exist, then print in a single line \"<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>read.meexample.txtb.cpp<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br/>read.m<br/>eexample.t<br/>xtb.cpp<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>version.infontldrcontestdata.zip<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<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=\"9ac7c2f2763087accca06e3f17ec9493\"/>\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=\"e25a2e8453e479693c0806119fdba17b9f05c3f0\"/>\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/174\">VK Cup 2012 Round 3 (Unofficial Div. 2 Edition)</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=\"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=\"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=\"Difficulty\">\r\n 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both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4303\" title=\"VK Cup 2012 Round 3 — Разбор\" 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=\"663\" resourceName=\"VK Cup 2012 Round 3 — Разбор\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/174\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/174/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/174/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/174/status\">Status</a></li>\r\n 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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_3dd750bf2db5940697f529673b20577a979d80d9\">\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. File List</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>Eudokimus, a system administrator is in trouble again. As a result of an error in some script, a list of names of very important files has been damaged. Since they were files in the BerFS file system, it is known that each file name has a form "<span class=\"tex-font-style-tt\">name.ext</span>", where: </p><ul> <li> <span class=\"tex-font-style-tt\">name</span> is a string consisting of lowercase Latin letters, its length is from 1 to 8 characters; </li><li> <span class=\"tex-font-style-tt\">ext</span> is a string consisting of lowercase Latin letters, its length is from 1 to 3 characters. </li></ul><p>For example, "<span class=\"tex-font-style-tt\">read.me</span>", "<span class=\"tex-font-style-tt\">example.txt</span>" and "<span class=\"tex-font-style-tt\">b.cpp</span>" are valid file names and "<span class=\"tex-font-style-tt\">version.info</span>", "<span class=\"tex-font-style-tt\">ntldr</span>" and "<span class=\"tex-font-style-tt\">contestdata.zip</span>" are not.</p><p>Damage to the list meant that all the file names were recorded one after another, without any separators. So now Eudokimus has a single string.</p><p>Eudokimus needs to set everything right as soon as possible. He should divide the resulting string into parts so that each part would be a valid file name in BerFS. Since Eudokimus has already proved that he is not good at programming, help him. The resulting file list can contain the same file names.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input data consists of a single string <span class=\"tex-span\"><i>s</i></span>, its length is from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">4·10<sup class=\"upper-index\">5</sup></span> characters. The string can contain only lowercase Latin letters ('<span class=\"tex-font-style-tt\">a</span>' - '<span class=\"tex-font-style-tt\">z</span>') and periods ('<span class=\"tex-font-style-tt\">.</span>').</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print "<span class=\"tex-font-style-tt\">YES</span>" (without the quotes), if it is possible to divide <span class=\"tex-span\"><i>s</i></span> into parts as required. In this case, the following lines should contain the parts of the required partition, one per line in the order in which they appear in <span class=\"tex-span\"><i>s</i></span>. The required partition can contain the same file names. If there are multiple solutions, print any of them.</p><p>If the solution does not exist, then print in a single line "<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>read.meexample.txtb.cpp<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br />read.m<br />eexample.t<br />xtb.cpp<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>version.infontldrcontestdata.zip<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<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 = 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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=''>13:55:07</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='f8539b4f84c368e0f04723c04d0da3b3'/>\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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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/Burunduk1\">Burunduk1</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Burunduk1\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Burunduk1\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Burunduk1\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Burunduk1\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Burunduk1\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Burunduk1\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Burunduk1\" style=\"text-decoration:none;color:black !important;\">Burunduk1'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=\"4317\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4303\"> <p>VK Cup 2012 Round 3 — Разбор</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a>,\r\n <span class=\"format-humantime\" title=\"Apr/08/2012 22:13\">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><a href=\"/contest/164/problem/A\" title=\"VK Cup 2012 Раунд 3\">164A - Переменная, или Туда и обратно</a></p><p><strong>Кратко о решении — dfs, O(E).</strong></p><p>Пустим поиск в глубину из всех вершин, где переменная присваивается. Пометим все посещенные.</p><p>Пустим поиск в глубину по обратным ребрам из всех вершин, где переменная используется. Запретим ему проходить по вершинам, где переменная присваивается. Пометим все посещенные.</p><p>Вершины помеченные оба раза — это и есть те вершины, где состояние Васи кого-то волнует</p><p><a href=\"/contest/164/problem/B\" title=\"VK Cup 2012 Раунд 3\">164B - Древние берляндские иероглифы</a></p><p><strong>Кратко о решении — метод двух указателей, O(N).</strong></p><p>Давайте для удобства предположим, что каждый символ в каждой строке встречается ровно один раз.</p><p>Тогда у нас есть перестановка <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (позиция во второй строке <span class=\"tex-span\"><i>i</i></span>-го символа первой строки)</p><p>Решение за квадрат теперь такое: фиксируем начало подстроки и идем по ней вперед, при этом параллельно идем по подпоследовательности и следим, что и там, и там мы не прошли больше круга.</p><p>Решение за линию.</p><p>Будем теперь идти двумя указателями "начало подстроки" и "конец подстроки". Параллельно будем хранить очередь — текущая парная подпоследовательность. В очереди все <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> обязательно возрастают (этого не сложно достичь, т.к. можно прибавлять к <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> число <span class=\"tex-span\"><i>n</i></span> столько раз, сколько нужно. То что подпоследовательность не зациклилась проверяется так <span class=\"tex-span\"><i>queue</i>.<i>first</i> - <i>queue</i>.<i>last</i> < <i>n</i></span>. Значит, мы можем двигать конец подстроки вперед, пока это неравенство выполнено. Как только конец подстроки нельзя увеличить, увеличиваем начало. Заметим, что начало и конец подстроки также двигаются по кругу.</p><p>Альтернативное решение:</p><p>После того, как мы увидели перестановку <span class=\"tex-span\"><i>p</i></span>, можно воспользоваться методом двоичных подъемов и получить решение за O(NlogN), которое тоже получало Accepted.</p><p><a href=\"/contest/164/problem/C\" title=\"VK Cup 2012 Раунд 3\">164C - Автоматное программирование</a></p><p><strong>Кратко о решении — MinCost flow, O(<span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> K) или O(NlogN K).</strong></p><p>Самое главное было — увидеть граф, где вершины = задания, множества заданий, выполняемые автоматами = вершиннонепересекающиеся пути, а ребра можно было строить двумя способами (см. ниже).</p><p>Как сделать пути вершиннонепересекающимися? Раздвоить вершины.</p><p>Как добавить стоимость? Между двумя половинками вершины должна быть стоимость <span class=\"tex-span\"> - <i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Первый способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> : вершины A, B соединены ребром, если после задания A можно успеть выполнить задание B тем же автоматом. Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Второй способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">2</sub></span> : все вершины упорядочены по <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> из вершины i ведут два ребра — в <span class=\"tex-span\"><i>i</i> + 1</span> (не берем <span class=\"tex-span\"><i>i</i></span> задание, пробуем взять следующее) и в вершину с минимальным <span class=\"tex-span\"><i>j</i></span> : <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub> ≥ <i>s</i><sub class=\"lower-index\"><i>i</i></sub> + <i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (берем задание, переходим к минимальному из возможных следующих). Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span>.</p><p>Если вы пользовались первым способом и для поиска пути реализовали одну из вариаций алгоритма Форда-Беллмана, то вы могли получить TL. Собственно пока из-за того, что на java все медленно, TL не подняли, все Форд-Беллманы кроме одного особенного получали заслуженный TL.</p><p>Чтобы в <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> использовать Дейкстру с потенциалами, удобнее всего было заметить, что граф ацикличен и первый раз расстояния посчитать за O(E).</p><p><a href=\"/contest/164/problem/D\" title=\"VK Cup 2012 Раунд 3\">164D - Минимальный диаметр</a></p><p><strong>Кратко о решении — бинпоиск по ответу, а внутри перебор за O(Fib(K)).</strong></p><p>Правильное решение состояло из четырех несложных идей:</p><p>1) Нужно из <span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> ребер покрыть удаленными вершинами сколько то максимальных. Когда мы покрываем еще не покрытое ребро, у нас 2 варианта это сделать — выбрать 1 конец, выбрать второй конец. Эта идея сама по себе давала асимптотику <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>K</i></sup> * <i>N</i>)</span>.</p><p>2) Если сделать бинпоиск по ответу, то мы решаем более простую задачу: можно ли покрыть первые X ребер K вершинами? Т.е. правда ли, что размер контролирующего множества в таком графе не более K. </p><p>3) Если мы теперь внутри бинпоиска не берем какую-то вершину, то мы должны брать всех ее соседей в уменьшенном графе. Из этого можно сделать 2 вывода: во-первых, если есть вершина степени больше чем K, ее брать обязательно, во-вторых, не выгодно брать вершину степени 1.</p><p>4) Теперь решение работает за log * Fib(K) * K, где log — константа от бинпоиска, Fib(K) — K-е число Фибоначчи, K --- максимальная степень вершины в уменьшенном графе.</p><p>Почему Fib(K)? Теперь, когда мы делаем выбор, в одной ветке рекурсии K уменьшается на 1, а в другой хотя бы на 2... На лицо числа Фибоначчи.</p><p>P.S. Из похожих задач я знаю вот эту: <a href=\"http://neerc.ifmo.ru/school/archive/2009-2010/ru-olymp-roi-2010-statements.rar\">задача 2 с РОИ 2009-2010</a></p><p><a href=\"/contest/164/problem/E\" title=\"VK Cup 2012 Раунд 3\">164E - Поликарп и работы</a></p><p><strong>Кратко о решении — жадность + куча запросов на отрезке, асимптотика = O(NlogN).</strong></p><p>В этой задаче так и не получилось написать очевидное условие...</p><p>Расскажу некоторую легенду, чтобы дать понять, что задачка не искусственна, взята из "реальной жизни".</p><p>Все вы читали задачу C. Давайте чуть поменяем ее, скажем, что автомат у нас один, а работа должна начаться не раньше <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, закончиться на позже <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, а времени на нее уйдет <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Рассмотрим случай, когда <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> возрастают.</p><p>Попробуем придумать жадное решение: отсортируем все работы по <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и будем пытаться "брать". Если можно взять, то выполнять работу будем в минимально возможный момент времени.</p><p>Это жадное решение не сложно завалить тестом (L=1, R=10, T=10), (L=2,R=11,T=5), (L=3,R=12,T=5).</p><p>Поэтому давайте жадность улучшим, попробуем, если добавить в конец не получается менять на кого-нибудь так, чтобы правый конец (последний использованный момент времени) максимально уменьшился.</p><p>Собственно задача E состояла в моделировании процесса. В том, чтобы запрограммировать эту жадность.</p><p><strong>Итак, решение:</strong></p><p>Для каждого отрезка определим величину <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>i</i></sub></span> = <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> — <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> (насколько можно отрезок подвинуть влево).</p><p>У нас уже есть <span class=\"tex-span\"><i>k</i></span> отрезков. Добавляем <span class=\"tex-span\"><i>k</i> + 1</span>-й, не получается. Пробуем сделать замену. Перебираем все отрезки в порядке уменьшения индекса, смотрим, насколько уменьшится правый конец.</p><p>Это min(<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>, min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Т.е. ни один из отрезков из 1..i уже не даст ответ лучше, чем min(max по j=i+1..k (<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>), min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Зачем я выдумал этот максимум? Дело в том, что под минимумом теперь две функции, убывающая и возрастающая. Значит, максимум можно искать бинарным или троичным поиском.</p><p>Следующая идея заключается в том, что когда мы нашли оптимальную замену <span class=\"tex-span\"><i>besti</i></span>, то чтобы пересчитать все <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>, достаточно сделать вычитание на отрезке besti+1..k</p><p>Полученное решение имеет асимптотику <span class=\"tex-span\"><i>O</i>(<i>Nlog</i><sup class=\"upper-index\">2</sup><i>N</i>)</span>. Его можно улучшить до <span class=\"tex-span\"><i>O</i>(<i>NlogN</i>)</span>, заменив бинпоиск, а внутри него обращение к дереву поиска или дереву отрезков на один спуск по дереву.</p><p><strong>UPD:</strong></p><p><strong>По просьбам участников выкладываю "разбор" задач A,B,C второго дивизиона.</strong></p><p>Задачи второго дивизиона я не готовил, не читал, не решал. Но вроде бы, если почитать, они решаются так, как описано ниже. Так что разбор второго дивизиона не стоит воспринимать как авторский, это просто рассказ "как бы я решал эти задачки". Надеюсь, нигде не наврал.</p><p><a href=\"https://codeforces.com/contest/174/problem/A\">Задача A</a></p><p>X = (<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></span> + b) / n.</p><p>Если <span class=\"tex-span\"><i>X</i></span> <strong>меньше</strong> максимального <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нельзя сделать так, как просят. Иначе нужно вывести числа X — <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/B\">Задача B</a></p><p><strong>Решение #1, жадное:</strong> </p><p>Если между двумя точками больше 11 или меньше 2 символов, то нельзя так разрезать.</p><p>Если перед первой точкой больше 8 символов, то нельзя так разрезать.</p><p>Если между после последней точки больше 3 символов, то нельзя так разрезать.</p><p>А иначе режем жадно :-) Если количество символов между двумя точками равно X, то разрез проводится в позиции min(8,X-1).</p><p><strong>Решение #2, DP:</strong> </p><p>is[i] — можем ли мы разрезать префикс длины <span class=\"tex-span\"><i>i</i></span>.</p><p>Изначально is[0] = 1, остальные нули.</p><p>Теперь перебираем <span class=\"tex-span\"><i>i</i></span> в порядке возрастания и если is[i] = 1, пытаемся сделать переход в <span class=\"tex-span\"><i>i</i> + 1</span>..<span class=\"tex-span\"><i>i</i> + 12</span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/C\">Задача C</a></p><p>Основная идея — жадность.</p><p>Если минимум на всем массиве равен нулю, то задача естественным образом распадается на подзадачи, а иначе нужно уменьшить весь отрезок на 1.</p><p><strong>Решение #1, ищем минимум</strong></p><p>Ищем минимум в массиве, вычитаем 1 из всего массива <span class=\"tex-span\"><i>min</i></span> раз, задача распадается на несколько (т.е. в каждый момент времени, задача = отрезок исходного массива). Минимум на отрезке нужно искать быстро, за O(logN), например.</p><p><strong>Решение #2, простое</strong></p><p>Будем идти слева направо и хранить, сколько у нас отрезков уже начато торчит налево, пусть это X. Если <span class=\"tex-span\"><i>X</i> < <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нужно начать несколько новых отрезков, если же <span class=\"tex-span\"><i>X</i> > <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то несколько уже начатых нужно закончить в позиции <span class=\"tex-span\"><i>i</i> - 1</span>. Начатые отрезки можно хранить в стэке. Хранить, конечно, нужно только позицию начала. Новый <span class=\"tex-span\"><i>X</i></span> будет равен <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><strong>Конец.</strong></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-148-4317\").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: \"148\",\n blogEntryId: \"4303\",\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=vkcup2012\" class=\"tag notice\" style=\"text-decoration: none;\">vkcup2012</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round3\" class=\"tag notice\" style=\"text-decoration: none;\">round3</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=%D1%80%D0%B0%D0%B7%D0%B1%D0%BE%D1%80\" class=\"tag notice\" style=\"text-decoration: none;\">разбор</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-4317\"><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'>+70</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4317\"><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/Burunduk1\"><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/Burunduk1\">\n Burunduk1\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=\"Apr/08/2012 22:13\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4303#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/4303#comments\">\n 9\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=\"4327\">\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 (8)</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=\"87633\" 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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87633\" href=\"?#comment-87633\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87633\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87633\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for writing up this. Can we expect an English version? </p><p>With Google translate, 164D's method is showed as "binpoisk to answer", what does "binpoisk" mean? Is it same as binary search?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87633 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87633 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87633\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87634\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/andreyv\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5720/avatar/26e7479dac2e8287.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/andreyv\" title=\"Expert andreyv\" class=\"rated-user user-blue\">andreyv</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87634\" href=\"?#comment-87634\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87634\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"5720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87634\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, it's an abbreviation of the two words.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87634 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87634 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87634\">\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=\"87658\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Burunduk1\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/347/avatar/8e55ad6d55eef9fa.jpg'/> </a>\n <div><a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 06:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87658\" href=\"?#comment-87658\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87658\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"347\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87658\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes. Binary Search = Binarniy Poisk = Binpoisk.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87658 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87658 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87658\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87674\" commentParentId=\"87658\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 20:26\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87674\" href=\"?#comment-87674\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87658\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87674\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87674\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks to both of you.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87674 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87674 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87674\">\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=\"541075\" 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/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/06/2019 13:44\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541075\" href=\"?#comment-541075\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541075\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541075\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Could anyone tell me a detailed explanation about dp approach for problem B. I'am learning DP.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541075 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541075 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541075\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"541309\" commentParentId=\"541075\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/07/2019 16:05\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541309\" href=\"?#comment-541309\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-541075\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541309\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541309\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/174/submission/60219361\">My solution</a> for problem B using DP approach!!! </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541309 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541309 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541309\">\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=\"591779\" 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/kesh4281\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/kesh4281\" title=\"Candidate Master kesh4281\" class=\"rated-user user-violet\">kesh4281</a></div>\n </div>\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/23/2020 13:18\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-591779\" href=\"?#comment-591779\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"591779\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"851343\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-591779\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Problem C, there are some good comments in announcement section as well. start=si finish=si+ti so times which are important are starts and finishes only. First coordinate compress all the times (starts and finishes) now let we have times like t1 t2 t3... t2n (at max we can have 2*n times) Let there be x distinct time. now connect vertices ti to ti+1 for all 1<=i<=x-1 with capacity k, cost 0 connect vertices ta to tb if we have a task that started at ta and ends at tb-1 (Read question carefully, a task starts at si and finishes at si+ti-1, and at si+ti machine is free). Capacity=1, Cost= -Cost of edge.</p><p>Now it becomes mincost maxflow problem with max flow upto k. If u didnt get it then just above graph once for sample input. u will surely understand.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-591779 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-591779 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-591779\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1039946\" 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/nonrice\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2487084/avatar/f9f0266eade11795.jpg'/> </a>\n <div><a href=\"/profile/nonrice\" title=\"Expert nonrice\" class=\"rated-user user-blue\">nonrice</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/22/2023 19:35\">4 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1039946\" href=\"?#comment-1039946\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1039946\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2487084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1039946\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did reverse version (maximum to minimum) way in C-Range Increments using dsu</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1039946 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1039946 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1039946\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4327\" 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Range Increments"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Range Increments</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>Polycarpus is an amateur programmer. Now he is analyzing a friend's program. He has already found there the function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>, that adds <span class=\"tex-font-style-tt\">1</span> to each element of some array <span class=\"tex-span\"><i>a</i></span> for all indexes in the segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>. In other words, this function does the following: </p><pre class=\"verbatim\"><br/>function rangeIncrement(l, r)<br/> for i := l .. r do<br/> a[i] = a[i] + 1<br/></pre><p>Polycarpus knows the state of the array <span class=\"tex-span\"><i>a</i></span> after a series of function calls. He wants to determine the minimum number of function calls that lead to such state. In addition, he wants to find what function calls are needed in this case. It is guaranteed that the required number of calls does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p><p>Before calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span> all array elements equal zero.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the length of the array <span class=\"tex-span\"><i>a</i>[1... <i>n</i>]</span>. </p><p>The second line contains its integer space-separated elements, <span class=\"tex-span\"><i>a</i>[1], <i>a</i>[2], ..., <i>a</i>[<i>n</i>]</span> (<span class=\"tex-span\">0 ≤ <i>a</i>[<i>i</i>] ≤ 10<sup class=\"upper-index\">5</sup></span>) after some series of function calls <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>. </p><p>It is guaranteed that at least one element of the array is positive. It is guaranteed that the answer contains no more than <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print on the first line <span class=\"tex-span\"><i>t</i></span> — the minimum number of calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>, that lead to the array from the input data. It is guaranteed that this number will turn out not more than <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p><p>Then print <span class=\"tex-span\"><i>t</i></span> lines — the descriptions of function calls, one per line. Each line should contain two integers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub>, <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>) — the arguments of the <span class=\"tex-span\"><i>i</i></span>-th call <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>. Calls can be applied in any order.</p><p>If there are multiple solutions, you are allowed to 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>6<br/>1 2 1 1 4 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/>2 2<br/>5 5<br/>5 5<br/>5 5<br/>1 6<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>1 0 1 0 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/>1 1<br/>3 3<br/>5 5<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The first sample requires a call for the entire array, and four additional calls:</p><ul> <li> one for the segment [2,2] (i.e. the second element of the array), </li><li> three for the segment [5,5] (i.e. the fifth element of the array). </li></ul></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=\"61d9db59d148ddca61fd0511485842b0\"/>\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 - 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=\"e25a2e8453e479693c0806119fdba17b9f05c3f0\"/>\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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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_3a9410657aa6dd23b197c96a7a53840f8a1c9e58\">\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. Range Increments</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>Polycarpus is an amateur programmer. Now he is analyzing a friend's program. He has already found there the function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>, that adds <span class=\"tex-font-style-tt\">1</span> to each element of some array <span class=\"tex-span\"><i>a</i></span> for all indexes in the segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>. In other words, this function does the following: </p><pre class=\"verbatim\"><br />function rangeIncrement(l, r)<br /> for i := l .. r do<br /> a[i] = a[i] + 1<br /></pre><p>Polycarpus knows the state of the array <span class=\"tex-span\"><i>a</i></span> after a series of function calls. He wants to determine the minimum number of function calls that lead to such state. In addition, he wants to find what function calls are needed in this case. It is guaranteed that the required number of calls does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p><p>Before calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span> all array elements equal zero.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the length of the array <span class=\"tex-span\"><i>a</i>[1... <i>n</i>]</span>. </p><p>The second line contains its integer space-separated elements, <span class=\"tex-span\"><i>a</i>[1], <i>a</i>[2], ..., <i>a</i>[<i>n</i>]</span> (<span class=\"tex-span\">0 ≤ <i>a</i>[<i>i</i>] ≤ 10<sup class=\"upper-index\">5</sup></span>) after some series of function calls <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>. </p><p>It is guaranteed that at least one element of the array is positive. It is guaranteed that the answer contains no more than <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print on the first line <span class=\"tex-span\"><i>t</i></span> — the minimum number of calls of function <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>, that lead to the array from the input data. It is guaranteed that this number will turn out not more than <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p><p>Then print <span class=\"tex-span\"><i>t</i></span> lines — the descriptions of function calls, one per line. Each line should contain two integers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub>, <i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>) — the arguments of the <span class=\"tex-span\"><i>i</i></span>-th call <span class=\"tex-font-style-tt\">rangeIncrement(l, r)</span>. Calls can be applied in any order.</p><p>If there are multiple solutions, you are allowed to 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>6<br />1 2 1 1 4 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br />2 2<br />5 5<br />5 5<br />5 5<br />1 6<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />1 0 1 0 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br />1 1<br />3 3<br />5 5<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The first sample requires a call for the entire array, and four additional calls:</p><ul> <li> one for the segment [2,2] (i.e. the second element of the array), </li><li> three for the segment [5,5] (i.e. the fifth element of the array). </li></ul></div></div></div>\r\n</div>\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=''>13:55:07</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='f8539b4f84c368e0f04723c04d0da3b3'/>\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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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/Burunduk1\">Burunduk1</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Burunduk1\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Burunduk1\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Burunduk1\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Burunduk1\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Burunduk1\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Burunduk1\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Burunduk1\" style=\"text-decoration:none;color:black !important;\">Burunduk1'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=\"4317\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4303\"> <p>VK Cup 2012 Round 3 — Разбор</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a>,\r\n <span class=\"format-humantime\" title=\"Apr/08/2012 22:13\">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><a href=\"/contest/164/problem/A\" title=\"VK Cup 2012 Раунд 3\">164A - Переменная, или Туда и обратно</a></p><p><strong>Кратко о решении — dfs, O(E).</strong></p><p>Пустим поиск в глубину из всех вершин, где переменная присваивается. Пометим все посещенные.</p><p>Пустим поиск в глубину по обратным ребрам из всех вершин, где переменная используется. Запретим ему проходить по вершинам, где переменная присваивается. Пометим все посещенные.</p><p>Вершины помеченные оба раза — это и есть те вершины, где состояние Васи кого-то волнует</p><p><a href=\"/contest/164/problem/B\" title=\"VK Cup 2012 Раунд 3\">164B - Древние берляндские иероглифы</a></p><p><strong>Кратко о решении — метод двух указателей, O(N).</strong></p><p>Давайте для удобства предположим, что каждый символ в каждой строке встречается ровно один раз.</p><p>Тогда у нас есть перестановка <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (позиция во второй строке <span class=\"tex-span\"><i>i</i></span>-го символа первой строки)</p><p>Решение за квадрат теперь такое: фиксируем начало подстроки и идем по ней вперед, при этом параллельно идем по подпоследовательности и следим, что и там, и там мы не прошли больше круга.</p><p>Решение за линию.</p><p>Будем теперь идти двумя указателями "начало подстроки" и "конец подстроки". Параллельно будем хранить очередь — текущая парная подпоследовательность. В очереди все <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> обязательно возрастают (этого не сложно достичь, т.к. можно прибавлять к <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> число <span class=\"tex-span\"><i>n</i></span> столько раз, сколько нужно. То что подпоследовательность не зациклилась проверяется так <span class=\"tex-span\"><i>queue</i>.<i>first</i> - <i>queue</i>.<i>last</i> < <i>n</i></span>. Значит, мы можем двигать конец подстроки вперед, пока это неравенство выполнено. Как только конец подстроки нельзя увеличить, увеличиваем начало. Заметим, что начало и конец подстроки также двигаются по кругу.</p><p>Альтернативное решение:</p><p>После того, как мы увидели перестановку <span class=\"tex-span\"><i>p</i></span>, можно воспользоваться методом двоичных подъемов и получить решение за O(NlogN), которое тоже получало Accepted.</p><p><a href=\"/contest/164/problem/C\" title=\"VK Cup 2012 Раунд 3\">164C - Автоматное программирование</a></p><p><strong>Кратко о решении — MinCost flow, O(<span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> K) или O(NlogN K).</strong></p><p>Самое главное было — увидеть граф, где вершины = задания, множества заданий, выполняемые автоматами = вершиннонепересекающиеся пути, а ребра можно было строить двумя способами (см. ниже).</p><p>Как сделать пути вершиннонепересекающимися? Раздвоить вершины.</p><p>Как добавить стоимость? Между двумя половинками вершины должна быть стоимость <span class=\"tex-span\"> - <i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Первый способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> : вершины A, B соединены ребром, если после задания A можно успеть выполнить задание B тем же автоматом. Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Второй способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">2</sub></span> : все вершины упорядочены по <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> из вершины i ведут два ребра — в <span class=\"tex-span\"><i>i</i> + 1</span> (не берем <span class=\"tex-span\"><i>i</i></span> задание, пробуем взять следующее) и в вершину с минимальным <span class=\"tex-span\"><i>j</i></span> : <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub> ≥ <i>s</i><sub class=\"lower-index\"><i>i</i></sub> + <i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (берем задание, переходим к минимальному из возможных следующих). Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span>.</p><p>Если вы пользовались первым способом и для поиска пути реализовали одну из вариаций алгоритма Форда-Беллмана, то вы могли получить TL. Собственно пока из-за того, что на java все медленно, TL не подняли, все Форд-Беллманы кроме одного особенного получали заслуженный TL.</p><p>Чтобы в <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> использовать Дейкстру с потенциалами, удобнее всего было заметить, что граф ацикличен и первый раз расстояния посчитать за O(E).</p><p><a href=\"/contest/164/problem/D\" title=\"VK Cup 2012 Раунд 3\">164D - Минимальный диаметр</a></p><p><strong>Кратко о решении — бинпоиск по ответу, а внутри перебор за O(Fib(K)).</strong></p><p>Правильное решение состояло из четырех несложных идей:</p><p>1) Нужно из <span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> ребер покрыть удаленными вершинами сколько то максимальных. Когда мы покрываем еще не покрытое ребро, у нас 2 варианта это сделать — выбрать 1 конец, выбрать второй конец. Эта идея сама по себе давала асимптотику <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>K</i></sup> * <i>N</i>)</span>.</p><p>2) Если сделать бинпоиск по ответу, то мы решаем более простую задачу: можно ли покрыть первые X ребер K вершинами? Т.е. правда ли, что размер контролирующего множества в таком графе не более K. </p><p>3) Если мы теперь внутри бинпоиска не берем какую-то вершину, то мы должны брать всех ее соседей в уменьшенном графе. Из этого можно сделать 2 вывода: во-первых, если есть вершина степени больше чем K, ее брать обязательно, во-вторых, не выгодно брать вершину степени 1.</p><p>4) Теперь решение работает за log * Fib(K) * K, где log — константа от бинпоиска, Fib(K) — K-е число Фибоначчи, K --- максимальная степень вершины в уменьшенном графе.</p><p>Почему Fib(K)? Теперь, когда мы делаем выбор, в одной ветке рекурсии K уменьшается на 1, а в другой хотя бы на 2... На лицо числа Фибоначчи.</p><p>P.S. Из похожих задач я знаю вот эту: <a href=\"http://neerc.ifmo.ru/school/archive/2009-2010/ru-olymp-roi-2010-statements.rar\">задача 2 с РОИ 2009-2010</a></p><p><a href=\"/contest/164/problem/E\" title=\"VK Cup 2012 Раунд 3\">164E - Поликарп и работы</a></p><p><strong>Кратко о решении — жадность + куча запросов на отрезке, асимптотика = O(NlogN).</strong></p><p>В этой задаче так и не получилось написать очевидное условие...</p><p>Расскажу некоторую легенду, чтобы дать понять, что задачка не искусственна, взята из "реальной жизни".</p><p>Все вы читали задачу C. Давайте чуть поменяем ее, скажем, что автомат у нас один, а работа должна начаться не раньше <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, закончиться на позже <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, а времени на нее уйдет <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Рассмотрим случай, когда <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> возрастают.</p><p>Попробуем придумать жадное решение: отсортируем все работы по <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и будем пытаться "брать". Если можно взять, то выполнять работу будем в минимально возможный момент времени.</p><p>Это жадное решение не сложно завалить тестом (L=1, R=10, T=10), (L=2,R=11,T=5), (L=3,R=12,T=5).</p><p>Поэтому давайте жадность улучшим, попробуем, если добавить в конец не получается менять на кого-нибудь так, чтобы правый конец (последний использованный момент времени) максимально уменьшился.</p><p>Собственно задача E состояла в моделировании процесса. В том, чтобы запрограммировать эту жадность.</p><p><strong>Итак, решение:</strong></p><p>Для каждого отрезка определим величину <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>i</i></sub></span> = <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> — <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> (насколько можно отрезок подвинуть влево).</p><p>У нас уже есть <span class=\"tex-span\"><i>k</i></span> отрезков. Добавляем <span class=\"tex-span\"><i>k</i> + 1</span>-й, не получается. Пробуем сделать замену. Перебираем все отрезки в порядке уменьшения индекса, смотрим, насколько уменьшится правый конец.</p><p>Это min(<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>, min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Т.е. ни один из отрезков из 1..i уже не даст ответ лучше, чем min(max по j=i+1..k (<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>), min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Зачем я выдумал этот максимум? Дело в том, что под минимумом теперь две функции, убывающая и возрастающая. Значит, максимум можно искать бинарным или троичным поиском.</p><p>Следующая идея заключается в том, что когда мы нашли оптимальную замену <span class=\"tex-span\"><i>besti</i></span>, то чтобы пересчитать все <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>, достаточно сделать вычитание на отрезке besti+1..k</p><p>Полученное решение имеет асимптотику <span class=\"tex-span\"><i>O</i>(<i>Nlog</i><sup class=\"upper-index\">2</sup><i>N</i>)</span>. Его можно улучшить до <span class=\"tex-span\"><i>O</i>(<i>NlogN</i>)</span>, заменив бинпоиск, а внутри него обращение к дереву поиска или дереву отрезков на один спуск по дереву.</p><p><strong>UPD:</strong></p><p><strong>По просьбам участников выкладываю "разбор" задач A,B,C второго дивизиона.</strong></p><p>Задачи второго дивизиона я не готовил, не читал, не решал. Но вроде бы, если почитать, они решаются так, как описано ниже. Так что разбор второго дивизиона не стоит воспринимать как авторский, это просто рассказ "как бы я решал эти задачки". Надеюсь, нигде не наврал.</p><p><a href=\"https://codeforces.com/contest/174/problem/A\">Задача A</a></p><p>X = (<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></span> + b) / n.</p><p>Если <span class=\"tex-span\"><i>X</i></span> <strong>меньше</strong> максимального <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нельзя сделать так, как просят. Иначе нужно вывести числа X — <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/B\">Задача B</a></p><p><strong>Решение #1, жадное:</strong> </p><p>Если между двумя точками больше 11 или меньше 2 символов, то нельзя так разрезать.</p><p>Если перед первой точкой больше 8 символов, то нельзя так разрезать.</p><p>Если между после последней точки больше 3 символов, то нельзя так разрезать.</p><p>А иначе режем жадно :-) Если количество символов между двумя точками равно X, то разрез проводится в позиции min(8,X-1).</p><p><strong>Решение #2, DP:</strong> </p><p>is[i] — можем ли мы разрезать префикс длины <span class=\"tex-span\"><i>i</i></span>.</p><p>Изначально is[0] = 1, остальные нули.</p><p>Теперь перебираем <span class=\"tex-span\"><i>i</i></span> в порядке возрастания и если is[i] = 1, пытаемся сделать переход в <span class=\"tex-span\"><i>i</i> + 1</span>..<span class=\"tex-span\"><i>i</i> + 12</span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/C\">Задача C</a></p><p>Основная идея — жадность.</p><p>Если минимум на всем массиве равен нулю, то задача естественным образом распадается на подзадачи, а иначе нужно уменьшить весь отрезок на 1.</p><p><strong>Решение #1, ищем минимум</strong></p><p>Ищем минимум в массиве, вычитаем 1 из всего массива <span class=\"tex-span\"><i>min</i></span> раз, задача распадается на несколько (т.е. в каждый момент времени, задача = отрезок исходного массива). Минимум на отрезке нужно искать быстро, за O(logN), например.</p><p><strong>Решение #2, простое</strong></p><p>Будем идти слева направо и хранить, сколько у нас отрезков уже начато торчит налево, пусть это X. Если <span class=\"tex-span\"><i>X</i> < <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нужно начать несколько новых отрезков, если же <span class=\"tex-span\"><i>X</i> > <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то несколько уже начатых нужно закончить в позиции <span class=\"tex-span\"><i>i</i> - 1</span>. Начатые отрезки можно хранить в стэке. Хранить, конечно, нужно только позицию начала. Новый <span class=\"tex-span\"><i>X</i></span> будет равен <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><strong>Конец.</strong></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-148-4317\").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: \"148\",\n blogEntryId: \"4303\",\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=vkcup2012\" class=\"tag notice\" style=\"text-decoration: none;\">vkcup2012</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round3\" class=\"tag notice\" style=\"text-decoration: none;\">round3</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=%D1%80%D0%B0%D0%B7%D0%B1%D0%BE%D1%80\" class=\"tag notice\" style=\"text-decoration: none;\">разбор</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-4317\"><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'>+70</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4317\"><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/Burunduk1\"><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/Burunduk1\">\n Burunduk1\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=\"Apr/08/2012 22:13\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4303#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/4303#comments\">\n 9\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=\"4327\">\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 (8)</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=\"87633\" 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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87633\" href=\"?#comment-87633\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87633\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87633\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for writing up this. Can we expect an English version? </p><p>With Google translate, 164D's method is showed as "binpoisk to answer", what does "binpoisk" mean? Is it same as binary search?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87633 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87633 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87633\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87634\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/andreyv\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5720/avatar/26e7479dac2e8287.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/andreyv\" title=\"Expert andreyv\" class=\"rated-user user-blue\">andreyv</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87634\" href=\"?#comment-87634\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87634\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"5720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87634\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, it's an abbreviation of the two words.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87634 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87634 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87634\">\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=\"87658\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Burunduk1\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/347/avatar/8e55ad6d55eef9fa.jpg'/> </a>\n <div><a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 06:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87658\" href=\"?#comment-87658\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87658\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"347\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87658\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes. Binary Search = Binarniy Poisk = Binpoisk.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87658 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87658 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87658\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87674\" commentParentId=\"87658\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 20:26\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87674\" href=\"?#comment-87674\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87658\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87674\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87674\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks to both of you.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87674 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87674 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87674\">\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=\"541075\" 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/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/06/2019 13:44\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541075\" href=\"?#comment-541075\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541075\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541075\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Could anyone tell me a detailed explanation about dp approach for problem B. I'am learning DP.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541075 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541075 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541075\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"541309\" commentParentId=\"541075\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/07/2019 16:05\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541309\" href=\"?#comment-541309\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-541075\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541309\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541309\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/174/submission/60219361\">My solution</a> for problem B using DP approach!!! </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541309 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541309 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541309\">\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=\"591779\" 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/kesh4281\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/kesh4281\" title=\"Candidate Master kesh4281\" class=\"rated-user user-violet\">kesh4281</a></div>\n </div>\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/23/2020 13:18\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-591779\" href=\"?#comment-591779\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"591779\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"851343\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-591779\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Problem C, there are some good comments in announcement section as well. start=si finish=si+ti so times which are important are starts and finishes only. First coordinate compress all the times (starts and finishes) now let we have times like t1 t2 t3... t2n (at max we can have 2*n times) Let there be x distinct time. now connect vertices ti to ti+1 for all 1<=i<=x-1 with capacity k, cost 0 connect vertices ta to tb if we have a task that started at ta and ends at tb-1 (Read question carefully, a task starts at si and finishes at si+ti-1, and at si+ti machine is free). Capacity=1, Cost= -Cost of edge.</p><p>Now it becomes mincost maxflow problem with max flow upto k. If u didnt get it then just above graph once for sample input. u will surely understand.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-591779 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-591779 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-591779\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1039946\" 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/nonrice\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2487084/avatar/f9f0266eade11795.jpg'/> </a>\n <div><a href=\"/profile/nonrice\" title=\"Expert nonrice\" class=\"rated-user user-blue\">nonrice</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/22/2023 19:35\">4 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1039946\" href=\"?#comment-1039946\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1039946\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2487084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1039946\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did reverse version (maximum to minimum) way in C-Range Increments using dsu</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1039946 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1039946 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1039946\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4327\" 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Variable, or There and Back Again"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Variable, or There and Back Again</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>Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used!</p><p>Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions.</p><p>A <span class=\"tex-font-style-it\">path</span> is a sequence of states <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, ..., <i>v</i><sub class=\"lower-index\"><i>x</i></sub></span>, where for any <span class=\"tex-span\">1 ≤ <i>i</i> < <i>x</i></span> exists a transition from <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> to <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>.</p><p>Vasya's value in state <span class=\"tex-span\"><i>v</i></span> is interesting to the world, if exists path <span class=\"tex-span\"><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></span> such, that <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub> = <i>v</i></span> for some <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ <i>k</i>)</span>, in state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span> Vasya gets assigned a value, in state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></span> Vasya is used and there is no state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (except for <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span>) where Vasya gets assigned a value.</p><p>Help Vasya, find the states in which Vasya's value is interesting to the world.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the numbers of states and transitions, correspondingly.</p><p>The second line contains space-separated <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub>, <i>f</i><sub class=\"lower-index\">2</sub>, ..., <i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>f</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 2</span>), <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>i</i></sub></span> described actions performed upon Vasya in state <span class=\"tex-span\"><i>i</i></span>: <span class=\"tex-span\">0</span> represents ignoring, <span class=\"tex-span\">1</span> — assigning a value, <span class=\"tex-span\">2</span> — using.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain space-separated pairs of integers <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>, <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>), each pair represents the transition from the state number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the state number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>. Between two states can be any number of transitions.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub>, <i>r</i><sub class=\"lower-index\">2</sub>, ..., <i>r</i><sub class=\"lower-index\"><i>n</i></sub></span>, separated by spaces or new lines. Number <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> should equal <span class=\"tex-span\">1</span>, if Vasya's value in state <span class=\"tex-span\"><i>i</i></span> is interesting to the world and otherwise, it should equal <span class=\"tex-span\">0</span>. The states are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> in the order, in which they are described 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>4 3<br/>1 0 0 2<br/>1 2<br/>2 3<br/>3 4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>1<br/>1<br/>1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br/>1 0 2<br/>1 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>0<br/>1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br/>2 0 1<br/>1 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/>0<br/>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 2 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 3 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 4; it includes all the states, so in all of them Vasya's value is interesting to the world.</p><p>The second sample the only path in which Vasya's value is interesting to the world is , — 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 3; state 2 is not included there.</p><p>In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world.</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=\"f5c9d4e371cb8802436671d07676a55b\"/>\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 - 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=\"e25a2e8453e479693c0806119fdba17b9f05c3f0\"/>\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/174\">VK Cup 2012 Round 3 (Unofficial Div. 2 Edition)</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='f5c9d4e371cb8802436671d07676a55b'/>\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/174/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=\"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=\"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\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='f5c9d4e371cb8802436671d07676a55b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1099\"/>\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='f5c9d4e371cb8802436671d07676a55b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1099\"/>\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/4302\" title=\"VK Cup 2012 Round 3\" target=\"_blank\">VK Cup 2012 Round 3</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"661:662\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4303\" title=\"VK Cup 2012 Round 3 — Разбор\" 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=\"663\" resourceName=\"VK Cup 2012 Round 3 — Разбор\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/174\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/174/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/174/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/174/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/174/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/174/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/174/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/174/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_03c211130a8f877bf7a54f055f89e97e464cd911\">\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. Variable, or There and Back Again</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>Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used!</p><p>Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions.</p><p>A <span class=\"tex-font-style-it\">path</span> is a sequence of states <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, ..., <i>v</i><sub class=\"lower-index\"><i>x</i></sub></span>, where for any <span class=\"tex-span\">1 ≤ <i>i</i> < <i>x</i></span> exists a transition from <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> to <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>.</p><p>Vasya's value in state <span class=\"tex-span\"><i>v</i></span> is interesting to the world, if exists path <span class=\"tex-span\"><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></span> such, that <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub> = <i>v</i></span> for some <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ <i>k</i>)</span>, in state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span> Vasya gets assigned a value, in state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></span> Vasya is used and there is no state <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (except for <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span>) where Vasya gets assigned a value.</p><p>Help Vasya, find the states in which Vasya's value is interesting to the world.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the numbers of states and transitions, correspondingly.</p><p>The second line contains space-separated <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub>, <i>f</i><sub class=\"lower-index\">2</sub>, ..., <i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>f</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 2</span>), <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>i</i></sub></span> described actions performed upon Vasya in state <span class=\"tex-span\"><i>i</i></span>: <span class=\"tex-span\">0</span> represents ignoring, <span class=\"tex-span\">1</span> — assigning a value, <span class=\"tex-span\">2</span> — using.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain space-separated pairs of integers <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>, <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>), each pair represents the transition from the state number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the state number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>. Between two states can be any number of transitions.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub>, <i>r</i><sub class=\"lower-index\">2</sub>, ..., <i>r</i><sub class=\"lower-index\"><i>n</i></sub></span>, separated by spaces or new lines. Number <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> should equal <span class=\"tex-span\">1</span>, if Vasya's value in state <span class=\"tex-span\"><i>i</i></span> is interesting to the world and otherwise, it should equal <span class=\"tex-span\">0</span>. The states are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> in the order, in which they are described 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>4 3<br />1 0 0 2<br />1 2<br />2 3<br />3 4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />1<br />1<br />1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br />1 0 2<br />1 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />0<br />1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br />2 0 1<br />1 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br />0<br />0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 2 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 3 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 4; it includes all the states, so in all of them Vasya's value is interesting to the world.</p><p>The second sample the only path in which Vasya's value is interesting to the world is , — 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 3; state 2 is not included there.</p><p>In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world.</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\", 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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='f8539b4f84c368e0f04723c04d0da3b3'/>\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/Burunduk1\">Burunduk1</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Burunduk1\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Burunduk1\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Burunduk1\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Burunduk1\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Burunduk1\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Burunduk1\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Burunduk1\" style=\"text-decoration:none;color:black !important;\">Burunduk1'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=\"4317\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4303\"> <p>VK Cup 2012 Round 3 — Разбор</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a>,\r\n <span class=\"format-humantime\" title=\"Apr/08/2012 22:13\">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><a href=\"/contest/164/problem/A\" title=\"VK Cup 2012 Раунд 3\">164A - Переменная, или Туда и обратно</a></p><p><strong>Кратко о решении — dfs, O(E).</strong></p><p>Пустим поиск в глубину из всех вершин, где переменная присваивается. Пометим все посещенные.</p><p>Пустим поиск в глубину по обратным ребрам из всех вершин, где переменная используется. Запретим ему проходить по вершинам, где переменная присваивается. Пометим все посещенные.</p><p>Вершины помеченные оба раза — это и есть те вершины, где состояние Васи кого-то волнует</p><p><a href=\"/contest/164/problem/B\" title=\"VK Cup 2012 Раунд 3\">164B - Древние берляндские иероглифы</a></p><p><strong>Кратко о решении — метод двух указателей, O(N).</strong></p><p>Давайте для удобства предположим, что каждый символ в каждой строке встречается ровно один раз.</p><p>Тогда у нас есть перестановка <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (позиция во второй строке <span class=\"tex-span\"><i>i</i></span>-го символа первой строки)</p><p>Решение за квадрат теперь такое: фиксируем начало подстроки и идем по ней вперед, при этом параллельно идем по подпоследовательности и следим, что и там, и там мы не прошли больше круга.</p><p>Решение за линию.</p><p>Будем теперь идти двумя указателями "начало подстроки" и "конец подстроки". Параллельно будем хранить очередь — текущая парная подпоследовательность. В очереди все <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> обязательно возрастают (этого не сложно достичь, т.к. можно прибавлять к <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> число <span class=\"tex-span\"><i>n</i></span> столько раз, сколько нужно. То что подпоследовательность не зациклилась проверяется так <span class=\"tex-span\"><i>queue</i>.<i>first</i> - <i>queue</i>.<i>last</i> < <i>n</i></span>. Значит, мы можем двигать конец подстроки вперед, пока это неравенство выполнено. Как только конец подстроки нельзя увеличить, увеличиваем начало. Заметим, что начало и конец подстроки также двигаются по кругу.</p><p>Альтернативное решение:</p><p>После того, как мы увидели перестановку <span class=\"tex-span\"><i>p</i></span>, можно воспользоваться методом двоичных подъемов и получить решение за O(NlogN), которое тоже получало Accepted.</p><p><a href=\"/contest/164/problem/C\" title=\"VK Cup 2012 Раунд 3\">164C - Автоматное программирование</a></p><p><strong>Кратко о решении — MinCost flow, O(<span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> K) или O(NlogN K).</strong></p><p>Самое главное было — увидеть граф, где вершины = задания, множества заданий, выполняемые автоматами = вершиннонепересекающиеся пути, а ребра можно было строить двумя способами (см. ниже).</p><p>Как сделать пути вершиннонепересекающимися? Раздвоить вершины.</p><p>Как добавить стоимость? Между двумя половинками вершины должна быть стоимость <span class=\"tex-span\"> - <i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Первый способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> : вершины A, B соединены ребром, если после задания A можно успеть выполнить задание B тем же автоматом. Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Второй способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">2</sub></span> : все вершины упорядочены по <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> из вершины i ведут два ребра — в <span class=\"tex-span\"><i>i</i> + 1</span> (не берем <span class=\"tex-span\"><i>i</i></span> задание, пробуем взять следующее) и в вершину с минимальным <span class=\"tex-span\"><i>j</i></span> : <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub> ≥ <i>s</i><sub class=\"lower-index\"><i>i</i></sub> + <i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (берем задание, переходим к минимальному из возможных следующих). Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span>.</p><p>Если вы пользовались первым способом и для поиска пути реализовали одну из вариаций алгоритма Форда-Беллмана, то вы могли получить TL. Собственно пока из-за того, что на java все медленно, TL не подняли, все Форд-Беллманы кроме одного особенного получали заслуженный TL.</p><p>Чтобы в <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> использовать Дейкстру с потенциалами, удобнее всего было заметить, что граф ацикличен и первый раз расстояния посчитать за O(E).</p><p><a href=\"/contest/164/problem/D\" title=\"VK Cup 2012 Раунд 3\">164D - Минимальный диаметр</a></p><p><strong>Кратко о решении — бинпоиск по ответу, а внутри перебор за O(Fib(K)).</strong></p><p>Правильное решение состояло из четырех несложных идей:</p><p>1) Нужно из <span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> ребер покрыть удаленными вершинами сколько то максимальных. Когда мы покрываем еще не покрытое ребро, у нас 2 варианта это сделать — выбрать 1 конец, выбрать второй конец. Эта идея сама по себе давала асимптотику <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>K</i></sup> * <i>N</i>)</span>.</p><p>2) Если сделать бинпоиск по ответу, то мы решаем более простую задачу: можно ли покрыть первые X ребер K вершинами? Т.е. правда ли, что размер контролирующего множества в таком графе не более K. </p><p>3) Если мы теперь внутри бинпоиска не берем какую-то вершину, то мы должны брать всех ее соседей в уменьшенном графе. Из этого можно сделать 2 вывода: во-первых, если есть вершина степени больше чем K, ее брать обязательно, во-вторых, не выгодно брать вершину степени 1.</p><p>4) Теперь решение работает за log * Fib(K) * K, где log — константа от бинпоиска, Fib(K) — K-е число Фибоначчи, K --- максимальная степень вершины в уменьшенном графе.</p><p>Почему Fib(K)? Теперь, когда мы делаем выбор, в одной ветке рекурсии K уменьшается на 1, а в другой хотя бы на 2... На лицо числа Фибоначчи.</p><p>P.S. Из похожих задач я знаю вот эту: <a href=\"http://neerc.ifmo.ru/school/archive/2009-2010/ru-olymp-roi-2010-statements.rar\">задача 2 с РОИ 2009-2010</a></p><p><a href=\"/contest/164/problem/E\" title=\"VK Cup 2012 Раунд 3\">164E - Поликарп и работы</a></p><p><strong>Кратко о решении — жадность + куча запросов на отрезке, асимптотика = O(NlogN).</strong></p><p>В этой задаче так и не получилось написать очевидное условие...</p><p>Расскажу некоторую легенду, чтобы дать понять, что задачка не искусственна, взята из "реальной жизни".</p><p>Все вы читали задачу C. Давайте чуть поменяем ее, скажем, что автомат у нас один, а работа должна начаться не раньше <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, закончиться на позже <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, а времени на нее уйдет <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Рассмотрим случай, когда <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> возрастают.</p><p>Попробуем придумать жадное решение: отсортируем все работы по <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и будем пытаться "брать". Если можно взять, то выполнять работу будем в минимально возможный момент времени.</p><p>Это жадное решение не сложно завалить тестом (L=1, R=10, T=10), (L=2,R=11,T=5), (L=3,R=12,T=5).</p><p>Поэтому давайте жадность улучшим, попробуем, если добавить в конец не получается менять на кого-нибудь так, чтобы правый конец (последний использованный момент времени) максимально уменьшился.</p><p>Собственно задача E состояла в моделировании процесса. В том, чтобы запрограммировать эту жадность.</p><p><strong>Итак, решение:</strong></p><p>Для каждого отрезка определим величину <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>i</i></sub></span> = <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> — <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> (насколько можно отрезок подвинуть влево).</p><p>У нас уже есть <span class=\"tex-span\"><i>k</i></span> отрезков. Добавляем <span class=\"tex-span\"><i>k</i> + 1</span>-й, не получается. Пробуем сделать замену. Перебираем все отрезки в порядке уменьшения индекса, смотрим, насколько уменьшится правый конец.</p><p>Это min(<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>, min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Т.е. ни один из отрезков из 1..i уже не даст ответ лучше, чем min(max по j=i+1..k (<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>), min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Зачем я выдумал этот максимум? Дело в том, что под минимумом теперь две функции, убывающая и возрастающая. Значит, максимум можно искать бинарным или троичным поиском.</p><p>Следующая идея заключается в том, что когда мы нашли оптимальную замену <span class=\"tex-span\"><i>besti</i></span>, то чтобы пересчитать все <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>, достаточно сделать вычитание на отрезке besti+1..k</p><p>Полученное решение имеет асимптотику <span class=\"tex-span\"><i>O</i>(<i>Nlog</i><sup class=\"upper-index\">2</sup><i>N</i>)</span>. Его можно улучшить до <span class=\"tex-span\"><i>O</i>(<i>NlogN</i>)</span>, заменив бинпоиск, а внутри него обращение к дереву поиска или дереву отрезков на один спуск по дереву.</p><p><strong>UPD:</strong></p><p><strong>По просьбам участников выкладываю "разбор" задач A,B,C второго дивизиона.</strong></p><p>Задачи второго дивизиона я не готовил, не читал, не решал. Но вроде бы, если почитать, они решаются так, как описано ниже. Так что разбор второго дивизиона не стоит воспринимать как авторский, это просто рассказ "как бы я решал эти задачки". Надеюсь, нигде не наврал.</p><p><a href=\"https://codeforces.com/contest/174/problem/A\">Задача A</a></p><p>X = (<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></span> + b) / n.</p><p>Если <span class=\"tex-span\"><i>X</i></span> <strong>меньше</strong> максимального <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нельзя сделать так, как просят. Иначе нужно вывести числа X — <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/B\">Задача B</a></p><p><strong>Решение #1, жадное:</strong> </p><p>Если между двумя точками больше 11 или меньше 2 символов, то нельзя так разрезать.</p><p>Если перед первой точкой больше 8 символов, то нельзя так разрезать.</p><p>Если между после последней точки больше 3 символов, то нельзя так разрезать.</p><p>А иначе режем жадно :-) Если количество символов между двумя точками равно X, то разрез проводится в позиции min(8,X-1).</p><p><strong>Решение #2, DP:</strong> </p><p>is[i] — можем ли мы разрезать префикс длины <span class=\"tex-span\"><i>i</i></span>.</p><p>Изначально is[0] = 1, остальные нули.</p><p>Теперь перебираем <span class=\"tex-span\"><i>i</i></span> в порядке возрастания и если is[i] = 1, пытаемся сделать переход в <span class=\"tex-span\"><i>i</i> + 1</span>..<span class=\"tex-span\"><i>i</i> + 12</span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/C\">Задача C</a></p><p>Основная идея — жадность.</p><p>Если минимум на всем массиве равен нулю, то задача естественным образом распадается на подзадачи, а иначе нужно уменьшить весь отрезок на 1.</p><p><strong>Решение #1, ищем минимум</strong></p><p>Ищем минимум в массиве, вычитаем 1 из всего массива <span class=\"tex-span\"><i>min</i></span> раз, задача распадается на несколько (т.е. в каждый момент времени, задача = отрезок исходного массива). Минимум на отрезке нужно искать быстро, за O(logN), например.</p><p><strong>Решение #2, простое</strong></p><p>Будем идти слева направо и хранить, сколько у нас отрезков уже начато торчит налево, пусть это X. Если <span class=\"tex-span\"><i>X</i> < <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нужно начать несколько новых отрезков, если же <span class=\"tex-span\"><i>X</i> > <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то несколько уже начатых нужно закончить в позиции <span class=\"tex-span\"><i>i</i> - 1</span>. Начатые отрезки можно хранить в стэке. Хранить, конечно, нужно только позицию начала. Новый <span class=\"tex-span\"><i>X</i></span> будет равен <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><strong>Конец.</strong></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-148-4317\").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: \"148\",\n blogEntryId: \"4303\",\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=vkcup2012\" class=\"tag notice\" style=\"text-decoration: none;\">vkcup2012</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round3\" class=\"tag notice\" style=\"text-decoration: none;\">round3</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=%D1%80%D0%B0%D0%B7%D0%B1%D0%BE%D1%80\" class=\"tag notice\" style=\"text-decoration: none;\">разбор</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-4317\"><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'>+70</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4317\"><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/Burunduk1\"><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/Burunduk1\">\n Burunduk1\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=\"Apr/08/2012 22:13\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4303#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/4303#comments\">\n 9\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=\"4327\">\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 (8)</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=\"87633\" 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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87633\" href=\"?#comment-87633\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87633\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87633\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for writing up this. Can we expect an English version? </p><p>With Google translate, 164D's method is showed as "binpoisk to answer", what does "binpoisk" mean? Is it same as binary search?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87633 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87633 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87633\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87634\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/andreyv\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5720/avatar/26e7479dac2e8287.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/andreyv\" title=\"Expert andreyv\" class=\"rated-user user-blue\">andreyv</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87634\" href=\"?#comment-87634\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87634\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"5720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87634\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, it's an abbreviation of the two words.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87634 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87634 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87634\">\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=\"87658\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Burunduk1\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/347/avatar/8e55ad6d55eef9fa.jpg'/> </a>\n <div><a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 06:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87658\" href=\"?#comment-87658\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87658\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"347\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87658\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes. Binary Search = Binarniy Poisk = Binpoisk.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87658 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87658 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87658\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87674\" commentParentId=\"87658\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 20:26\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87674\" href=\"?#comment-87674\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87658\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87674\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87674\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks to both of you.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87674 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87674 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87674\">\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=\"541075\" 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/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/06/2019 13:44\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541075\" href=\"?#comment-541075\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541075\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541075\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Could anyone tell me a detailed explanation about dp approach for problem B. I'am learning DP.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541075 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541075 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541075\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"541309\" commentParentId=\"541075\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/07/2019 16:05\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541309\" href=\"?#comment-541309\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-541075\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541309\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541309\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/174/submission/60219361\">My solution</a> for problem B using DP approach!!! </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541309 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541309 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541309\">\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=\"591779\" 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/kesh4281\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/kesh4281\" title=\"Candidate Master kesh4281\" class=\"rated-user user-violet\">kesh4281</a></div>\n </div>\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/23/2020 13:18\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-591779\" href=\"?#comment-591779\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"591779\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"851343\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-591779\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Problem C, there are some good comments in announcement section as well. start=si finish=si+ti so times which are important are starts and finishes only. First coordinate compress all the times (starts and finishes) now let we have times like t1 t2 t3... t2n (at max we can have 2*n times) Let there be x distinct time. now connect vertices ti to ti+1 for all 1<=i<=x-1 with capacity k, cost 0 connect vertices ta to tb if we have a task that started at ta and ends at tb-1 (Read question carefully, a task starts at si and finishes at si+ti-1, and at si+ti machine is free). Capacity=1, Cost= -Cost of edge.</p><p>Now it becomes mincost maxflow problem with max flow upto k. If u didnt get it then just above graph once for sample input. u will surely understand.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-591779 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-591779 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-591779\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1039946\" 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/nonrice\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2487084/avatar/f9f0266eade11795.jpg'/> </a>\n <div><a href=\"/profile/nonrice\" title=\"Expert nonrice\" class=\"rated-user user-blue\">nonrice</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/22/2023 19:35\">4 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1039946\" href=\"?#comment-1039946\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1039946\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2487084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1039946\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did reverse version (maximum to minimum) way in C-Range Increments using dsu</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1039946 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1039946 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1039946\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4327\" 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Ancient Berland Hieroglyphs"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Ancient Berland Hieroglyphs</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>Polycarpus enjoys studying Berland hieroglyphs. Once Polycarp got hold of two ancient Berland pictures, on each of which was drawn a circle of hieroglyphs. We know that no hieroglyph occurs twice in either the first or the second circle (but in can occur once in each of them).</p><p>Polycarpus wants to save these pictures on his laptop, but the problem is, laptops do not allow to write hieroglyphs circles. So Polycarp had to break each circle and write down all of its hieroglyphs in a clockwise order in one line. A line obtained from the first circle will be called <span class=\"tex-span\"><i>a</i></span>, and the line obtained from the second one will be called <span class=\"tex-span\"><i>b</i></span>.</p><p>There are quite many ways to break hieroglyphic circles, so Polycarpus chooses the method, that makes the length of the largest substring of string <span class=\"tex-span\"><i>a</i></span>, which occurs as a subsequence in string <span class=\"tex-span\"><i>b</i></span>, maximum.</p><p>Help Polycarpus — find the maximum possible length of the desired substring (subsequence) if the first and the second circles are broken optimally.</p><p>The <span class=\"tex-font-style-it\">length</span> of string <span class=\"tex-span\"><i>s</i></span> is the number of characters in it. If we denote the length of string <span class=\"tex-span\"><i>s</i></span> as <span class=\"tex-span\">|<i>s</i>|</span>, we can write the string as <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 <span class=\"tex-font-style-it\">substring</span> of <span class=\"tex-span\"><i>s</i></span> is a non-empty string <span class=\"tex-span\"><i>x</i> = <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>). For example, \"<span class=\"tex-font-style-tt\">code</span>\" and \"<span class=\"tex-font-style-tt\">force</span>\" are substrings of \"<span class=\"tex-font-style-tt\">codeforces</span>\", while \"<span class=\"tex-font-style-tt\">coders</span>\" is not. </p><p>A <span class=\"tex-font-style-it\">subsequence</span> of <span class=\"tex-span\"><i>s</i></span> is a non-empty string <span class=\"tex-span\"><i>y</i> = <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>y</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>y</i>|</sub></sub></span> (<span class=\"tex-span\">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>y</i>|</sub> ≤ |<i>s</i>|</span>). For example, \"<span class=\"tex-font-style-tt\">coders</span>\" is a subsequence of \"<span class=\"tex-font-style-tt\">codeforces</span>\".</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>a</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>b</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>l</i><sub class=\"lower-index\"><i>a</i></sub>, <i>l</i><sub class=\"lower-index\"><i>b</i></sub> ≤ 1000000</span>) — the number of hieroglyphs in the first and second circles, respectively.</p><p>Below, due to difficulties with encoding of Berland hieroglyphs, they are given as integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>.</p><p>The second line contains <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>a</i></sub></span> integers — the hieroglyphs in the first picture, in the clockwise order, starting with one of them.</p><p>The third line contains <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>b</i></sub></span> integers — the hieroglyphs in the second picture, in the clockwise order, starting with one of them.</p><p>It is guaranteed that the first circle doesn't contain a hieroglyph, which occurs twice. The second circle also has this property.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum length of the common substring and subsequence. If at any way of breaking the circles it does not exist, print <span class=\"tex-font-style-tt\">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>5 4<br/>1 2 3 4 5<br/>1 3 5 6<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 6<br/>1 3 5 2<br/>1 2 3 4 5 6<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>3 3<br/>1 2 3<br/>3 2 1<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 test Polycarpus picks a string that consists of hieroglyphs 5 and 1, and in the second sample — from hieroglyphs 1, 3 and 5.</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=\"90f5e8d4843a4272138a98c4bc7fd08c\"/>\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=\"e25a2e8453e479693c0806119fdba17b9f05c3f0\"/>\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=\"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='90f5e8d4843a4272138a98c4bc7fd08c'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1100\"/>\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='90f5e8d4843a4272138a98c4bc7fd08c'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1100\"/>\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/4302\" title=\"VK Cup 2012 Round 3\" target=\"_blank\">VK Cup 2012 Round 3</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"661:662\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4303\" title=\"VK Cup 2012 Round 3 — Разбор\" 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=\"663\" resourceName=\"VK Cup 2012 Round 3 — Разбор\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/174\">Problems</a></li>\r\n <li><a\r\n 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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=\"E\" data-uuid=\"ps_b6e517f369ef46d33d4268109bbd1525175fb983\">\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. Ancient Berland Hieroglyphs</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>Polycarpus enjoys studying Berland hieroglyphs. Once Polycarp got hold of two ancient Berland pictures, on each of which was drawn a circle of hieroglyphs. We know that no hieroglyph occurs twice in either the first or the second circle (but in can occur once in each of them).</p><p>Polycarpus wants to save these pictures on his laptop, but the problem is, laptops do not allow to write hieroglyphs circles. So Polycarp had to break each circle and write down all of its hieroglyphs in a clockwise order in one line. A line obtained from the first circle will be called <span class=\"tex-span\"><i>a</i></span>, and the line obtained from the second one will be called <span class=\"tex-span\"><i>b</i></span>.</p><p>There are quite many ways to break hieroglyphic circles, so Polycarpus chooses the method, that makes the length of the largest substring of string <span class=\"tex-span\"><i>a</i></span>, which occurs as a subsequence in string <span class=\"tex-span\"><i>b</i></span>, maximum.</p><p>Help Polycarpus — find the maximum possible length of the desired substring (subsequence) if the first and the second circles are broken optimally.</p><p>The <span class=\"tex-font-style-it\">length</span> of string <span class=\"tex-span\"><i>s</i></span> is the number of characters in it. If we denote the length of string <span class=\"tex-span\"><i>s</i></span> as <span class=\"tex-span\">|<i>s</i>|</span>, we can write the string as <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 <span class=\"tex-font-style-it\">substring</span> of <span class=\"tex-span\"><i>s</i></span> is a non-empty string <span class=\"tex-span\"><i>x</i> = <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>). For example, "<span class=\"tex-font-style-tt\">code</span>" and "<span class=\"tex-font-style-tt\">force</span>" are substrings of "<span class=\"tex-font-style-tt\">codeforces</span>", while "<span class=\"tex-font-style-tt\">coders</span>" is not. </p><p>A <span class=\"tex-font-style-it\">subsequence</span> of <span class=\"tex-span\"><i>s</i></span> is a non-empty string <span class=\"tex-span\"><i>y</i> = <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>y</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>y</i>|</sub></sub></span> (<span class=\"tex-span\">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>y</i>|</sub> ≤ |<i>s</i>|</span>). For example, "<span class=\"tex-font-style-tt\">coders</span>" is a subsequence of "<span class=\"tex-font-style-tt\">codeforces</span>".</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>a</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>b</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>l</i><sub class=\"lower-index\"><i>a</i></sub>, <i>l</i><sub class=\"lower-index\"><i>b</i></sub> ≤ 1000000</span>) — the number of hieroglyphs in the first and second circles, respectively.</p><p>Below, due to difficulties with encoding of Berland hieroglyphs, they are given as integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>.</p><p>The second line contains <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>a</i></sub></span> integers — the hieroglyphs in the first picture, in the clockwise order, starting with one of them.</p><p>The third line contains <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>b</i></sub></span> integers — the hieroglyphs in the second picture, in the clockwise order, starting with one of them.</p><p>It is guaranteed that the first circle doesn't contain a hieroglyph, which occurs twice. The second circle also has this property.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum length of the common substring and subsequence. If at any way of breaking the circles it does not exist, print <span class=\"tex-font-style-tt\">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>5 4<br />1 2 3 4 5<br />1 3 5 6<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 6<br />1 3 5 2<br />1 2 3 4 5 6<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>3 3<br />1 2 3<br />3 2 1<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 test Polycarpus picks a string that consists of hieroglyphs 5 and 1, and in the second sample — from hieroglyphs 1, 3 and 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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=''>13:55:07</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='f8539b4f84c368e0f04723c04d0da3b3'/>\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/Burunduk1\">Burunduk1</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Burunduk1\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Burunduk1\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Burunduk1\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Burunduk1\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Burunduk1\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Burunduk1\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Burunduk1\" style=\"text-decoration:none;color:black !important;\">Burunduk1'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=\"4317\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4303\"> <p>VK Cup 2012 Round 3 — Разбор</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a>,\r\n <span class=\"format-humantime\" title=\"Apr/08/2012 22:13\">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><a href=\"/contest/164/problem/A\" title=\"VK Cup 2012 Раунд 3\">164A - Переменная, или Туда и обратно</a></p><p><strong>Кратко о решении — dfs, O(E).</strong></p><p>Пустим поиск в глубину из всех вершин, где переменная присваивается. Пометим все посещенные.</p><p>Пустим поиск в глубину по обратным ребрам из всех вершин, где переменная используется. Запретим ему проходить по вершинам, где переменная присваивается. Пометим все посещенные.</p><p>Вершины помеченные оба раза — это и есть те вершины, где состояние Васи кого-то волнует</p><p><a href=\"/contest/164/problem/B\" title=\"VK Cup 2012 Раунд 3\">164B - Древние берляндские иероглифы</a></p><p><strong>Кратко о решении — метод двух указателей, O(N).</strong></p><p>Давайте для удобства предположим, что каждый символ в каждой строке встречается ровно один раз.</p><p>Тогда у нас есть перестановка <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (позиция во второй строке <span class=\"tex-span\"><i>i</i></span>-го символа первой строки)</p><p>Решение за квадрат теперь такое: фиксируем начало подстроки и идем по ней вперед, при этом параллельно идем по подпоследовательности и следим, что и там, и там мы не прошли больше круга.</p><p>Решение за линию.</p><p>Будем теперь идти двумя указателями "начало подстроки" и "конец подстроки". Параллельно будем хранить очередь — текущая парная подпоследовательность. В очереди все <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> обязательно возрастают (этого не сложно достичь, т.к. можно прибавлять к <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> число <span class=\"tex-span\"><i>n</i></span> столько раз, сколько нужно. То что подпоследовательность не зациклилась проверяется так <span class=\"tex-span\"><i>queue</i>.<i>first</i> - <i>queue</i>.<i>last</i> < <i>n</i></span>. Значит, мы можем двигать конец подстроки вперед, пока это неравенство выполнено. Как только конец подстроки нельзя увеличить, увеличиваем начало. Заметим, что начало и конец подстроки также двигаются по кругу.</p><p>Альтернативное решение:</p><p>После того, как мы увидели перестановку <span class=\"tex-span\"><i>p</i></span>, можно воспользоваться методом двоичных подъемов и получить решение за O(NlogN), которое тоже получало Accepted.</p><p><a href=\"/contest/164/problem/C\" title=\"VK Cup 2012 Раунд 3\">164C - Автоматное программирование</a></p><p><strong>Кратко о решении — MinCost flow, O(<span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> K) или O(NlogN K).</strong></p><p>Самое главное было — увидеть граф, где вершины = задания, множества заданий, выполняемые автоматами = вершиннонепересекающиеся пути, а ребра можно было строить двумя способами (см. ниже).</p><p>Как сделать пути вершиннонепересекающимися? Раздвоить вершины.</p><p>Как добавить стоимость? Между двумя половинками вершины должна быть стоимость <span class=\"tex-span\"> - <i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Первый способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> : вершины A, B соединены ребром, если после задания A можно успеть выполнить задание B тем же автоматом. Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Второй способ, граф <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">2</sub></span> : все вершины упорядочены по <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> из вершины i ведут два ребра — в <span class=\"tex-span\"><i>i</i> + 1</span> (не берем <span class=\"tex-span\"><i>i</i></span> задание, пробуем взять следующее) и в вершину с минимальным <span class=\"tex-span\"><i>j</i></span> : <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub> ≥ <i>s</i><sub class=\"lower-index\"><i>i</i></sub> + <i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> (берем задание, переходим к минимальному из возможных следующих). Тогда ребер <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span>.</p><p>Если вы пользовались первым способом и для поиска пути реализовали одну из вариаций алгоритма Форда-Беллмана, то вы могли получить TL. Собственно пока из-за того, что на java все медленно, TL не подняли, все Форд-Беллманы кроме одного особенного получали заслуженный TL.</p><p>Чтобы в <span class=\"tex-span\"><i>G</i><sub class=\"lower-index\">1</sub></span> использовать Дейкстру с потенциалами, удобнее всего было заметить, что граф ацикличен и первый раз расстояния посчитать за O(E).</p><p><a href=\"/contest/164/problem/D\" title=\"VK Cup 2012 Раунд 3\">164D - Минимальный диаметр</a></p><p><strong>Кратко о решении — бинпоиск по ответу, а внутри перебор за O(Fib(K)).</strong></p><p>Правильное решение состояло из четырех несложных идей:</p><p>1) Нужно из <span class=\"tex-span\"><i>N</i><sup class=\"upper-index\">2</sup></span> ребер покрыть удаленными вершинами сколько то максимальных. Когда мы покрываем еще не покрытое ребро, у нас 2 варианта это сделать — выбрать 1 конец, выбрать второй конец. Эта идея сама по себе давала асимптотику <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>K</i></sup> * <i>N</i>)</span>.</p><p>2) Если сделать бинпоиск по ответу, то мы решаем более простую задачу: можно ли покрыть первые X ребер K вершинами? Т.е. правда ли, что размер контролирующего множества в таком графе не более K. </p><p>3) Если мы теперь внутри бинпоиска не берем какую-то вершину, то мы должны брать всех ее соседей в уменьшенном графе. Из этого можно сделать 2 вывода: во-первых, если есть вершина степени больше чем K, ее брать обязательно, во-вторых, не выгодно брать вершину степени 1.</p><p>4) Теперь решение работает за log * Fib(K) * K, где log — константа от бинпоиска, Fib(K) — K-е число Фибоначчи, K --- максимальная степень вершины в уменьшенном графе.</p><p>Почему Fib(K)? Теперь, когда мы делаем выбор, в одной ветке рекурсии K уменьшается на 1, а в другой хотя бы на 2... На лицо числа Фибоначчи.</p><p>P.S. Из похожих задач я знаю вот эту: <a href=\"http://neerc.ifmo.ru/school/archive/2009-2010/ru-olymp-roi-2010-statements.rar\">задача 2 с РОИ 2009-2010</a></p><p><a href=\"/contest/164/problem/E\" title=\"VK Cup 2012 Раунд 3\">164E - Поликарп и работы</a></p><p><strong>Кратко о решении — жадность + куча запросов на отрезке, асимптотика = O(NlogN).</strong></p><p>В этой задаче так и не получилось написать очевидное условие...</p><p>Расскажу некоторую легенду, чтобы дать понять, что задачка не искусственна, взята из "реальной жизни".</p><p>Все вы читали задачу C. Давайте чуть поменяем ее, скажем, что автомат у нас один, а работа должна начаться не раньше <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, закончиться на позже <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, а времени на нее уйдет <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>. Рассмотрим случай, когда <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> возрастают.</p><p>Попробуем придумать жадное решение: отсортируем все работы по <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> и будем пытаться "брать". Если можно взять, то выполнять работу будем в минимально возможный момент времени.</p><p>Это жадное решение не сложно завалить тестом (L=1, R=10, T=10), (L=2,R=11,T=5), (L=3,R=12,T=5).</p><p>Поэтому давайте жадность улучшим, попробуем, если добавить в конец не получается менять на кого-нибудь так, чтобы правый конец (последний использованный момент времени) максимально уменьшился.</p><p>Собственно задача E состояла в моделировании процесса. В том, чтобы запрограммировать эту жадность.</p><p><strong>Итак, решение:</strong></p><p>Для каждого отрезка определим величину <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>i</i></sub></span> = <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> — <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> (насколько можно отрезок подвинуть влево).</p><p>У нас уже есть <span class=\"tex-span\"><i>k</i></span> отрезков. Добавляем <span class=\"tex-span\"><i>k</i> + 1</span>-й, не получается. Пробуем сделать замену. Перебираем все отрезки в порядке уменьшения индекса, смотрим, насколько уменьшится правый конец.</p><p>Это min(<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span>, min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Т.е. ни один из отрезков из 1..i уже не даст ответ лучше, чем min(max по j=i+1..k (<span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>), min по j=i+1..k (<span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>)).</p><p>Зачем я выдумал этот максимум? Дело в том, что под минимумом теперь две функции, убывающая и возрастающая. Значит, максимум можно искать бинарным или троичным поиском.</p><p>Следующая идея заключается в том, что когда мы нашли оптимальную замену <span class=\"tex-span\"><i>besti</i></span>, то чтобы пересчитать все <span class=\"tex-span\"><i>shift</i><sub class=\"lower-index\"><i>j</i></sub></span>, достаточно сделать вычитание на отрезке besti+1..k</p><p>Полученное решение имеет асимптотику <span class=\"tex-span\"><i>O</i>(<i>Nlog</i><sup class=\"upper-index\">2</sup><i>N</i>)</span>. Его можно улучшить до <span class=\"tex-span\"><i>O</i>(<i>NlogN</i>)</span>, заменив бинпоиск, а внутри него обращение к дереву поиска или дереву отрезков на один спуск по дереву.</p><p><strong>UPD:</strong></p><p><strong>По просьбам участников выкладываю "разбор" задач A,B,C второго дивизиона.</strong></p><p>Задачи второго дивизиона я не готовил, не читал, не решал. Но вроде бы, если почитать, они решаются так, как описано ниже. Так что разбор второго дивизиона не стоит воспринимать как авторский, это просто рассказ "как бы я решал эти задачки". Надеюсь, нигде не наврал.</p><p><a href=\"https://codeforces.com/contest/174/problem/A\">Задача A</a></p><p>X = (<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></span> + b) / n.</p><p>Если <span class=\"tex-span\"><i>X</i></span> <strong>меньше</strong> максимального <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нельзя сделать так, как просят. Иначе нужно вывести числа X — <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/B\">Задача B</a></p><p><strong>Решение #1, жадное:</strong> </p><p>Если между двумя точками больше 11 или меньше 2 символов, то нельзя так разрезать.</p><p>Если перед первой точкой больше 8 символов, то нельзя так разрезать.</p><p>Если между после последней точки больше 3 символов, то нельзя так разрезать.</p><p>А иначе режем жадно :-) Если количество символов между двумя точками равно X, то разрез проводится в позиции min(8,X-1).</p><p><strong>Решение #2, DP:</strong> </p><p>is[i] — можем ли мы разрезать префикс длины <span class=\"tex-span\"><i>i</i></span>.</p><p>Изначально is[0] = 1, остальные нули.</p><p>Теперь перебираем <span class=\"tex-span\"><i>i</i></span> в порядке возрастания и если is[i] = 1, пытаемся сделать переход в <span class=\"tex-span\"><i>i</i> + 1</span>..<span class=\"tex-span\"><i>i</i> + 12</span>.</p><p><a href=\"https://codeforces.com/contest/174/problem/C\">Задача C</a></p><p>Основная идея — жадность.</p><p>Если минимум на всем массиве равен нулю, то задача естественным образом распадается на подзадачи, а иначе нужно уменьшить весь отрезок на 1.</p><p><strong>Решение #1, ищем минимум</strong></p><p>Ищем минимум в массиве, вычитаем 1 из всего массива <span class=\"tex-span\"><i>min</i></span> раз, задача распадается на несколько (т.е. в каждый момент времени, задача = отрезок исходного массива). Минимум на отрезке нужно искать быстро, за O(logN), например.</p><p><strong>Решение #2, простое</strong></p><p>Будем идти слева направо и хранить, сколько у нас отрезков уже начато торчит налево, пусть это X. Если <span class=\"tex-span\"><i>X</i> < <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то нужно начать несколько новых отрезков, если же <span class=\"tex-span\"><i>X</i> > <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, то несколько уже начатых нужно закончить в позиции <span class=\"tex-span\"><i>i</i> - 1</span>. Начатые отрезки можно хранить в стэке. Хранить, конечно, нужно только позицию начала. Новый <span class=\"tex-span\"><i>X</i></span> будет равен <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p><strong>Конец.</strong></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-148-4317\").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: \"148\",\n blogEntryId: \"4303\",\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=vkcup2012\" class=\"tag notice\" style=\"text-decoration: none;\">vkcup2012</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round3\" class=\"tag notice\" style=\"text-decoration: none;\">round3</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=%D1%80%D0%B0%D0%B7%D0%B1%D0%BE%D1%80\" class=\"tag notice\" style=\"text-decoration: none;\">разбор</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-4317\"><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'>+70</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4317\"><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/Burunduk1\"><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/Burunduk1\">\n Burunduk1\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=\"Apr/08/2012 22:13\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4303#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/4303#comments\">\n 9\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=\"4327\">\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 (8)</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=\"87633\" 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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87633\" href=\"?#comment-87633\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87633\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87633\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for writing up this. Can we expect an English version? </p><p>With Google translate, 164D's method is showed as "binpoisk to answer", what does "binpoisk" mean? Is it same as binary search?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87633 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87633 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87633\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87634\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/andreyv\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5720/avatar/26e7479dac2e8287.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/andreyv\" title=\"Expert andreyv\" class=\"rated-user user-blue\">andreyv</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/09/2012 18:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87634\" href=\"?#comment-87634\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87634\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"5720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87634\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, it's an abbreviation of the two words.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87634 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87634 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87634\">\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=\"87658\" commentParentId=\"87633\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Burunduk1\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/347/avatar/8e55ad6d55eef9fa.jpg'/> </a>\n <div><a href=\"/profile/Burunduk1\" title=\"International Grandmaster Burunduk1\" class=\"rated-user user-red\">Burunduk1</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 06:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87658\" href=\"?#comment-87658\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87633\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87658\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"347\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-87658\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes. Binary Search = Binarniy Poisk = Binpoisk.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87658 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87658 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87658\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"87674\" commentParentId=\"87658\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/hacker007\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/hacker007\" title=\"Specialist hacker007\" class=\"rated-user user-cyan\">hacker007</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/10/2012 20:26\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-87674\" href=\"?#comment-87674\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-87658\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"87674\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"2067\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-87674\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks to both of you.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-87674 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-87674 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-87674\">\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=\"541075\" 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/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/06/2019 13:44\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541075\" href=\"?#comment-541075\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541075\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541075\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Could anyone tell me a detailed explanation about dp approach for problem B. I'am learning DP.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541075 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541075 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541075\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"541309\" commentParentId=\"541075\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Hd7\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Hd7\" title=\"Specialist Hd7\" class=\"rated-user user-cyan\">Hd7</a></div>\n </div>\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/07/2019 16:05\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-541309\" href=\"?#comment-541309\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-541075\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"541309\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"559666\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-541309\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/174/submission/60219361\">My solution</a> for problem B using DP approach!!! </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-541309 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-541309 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-541309\">\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=\"591779\" 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/kesh4281\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/kesh4281\" title=\"Candidate Master kesh4281\" class=\"rated-user user-violet\">kesh4281</a></div>\n </div>\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/23/2020 13:18\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-591779\" href=\"?#comment-591779\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"591779\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"851343\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-591779\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Problem C, there are some good comments in announcement section as well. start=si finish=si+ti so times which are important are starts and finishes only. First coordinate compress all the times (starts and finishes) now let we have times like t1 t2 t3... t2n (at max we can have 2*n times) Let there be x distinct time. now connect vertices ti to ti+1 for all 1<=i<=x-1 with capacity k, cost 0 connect vertices ta to tb if we have a task that started at ta and ends at tb-1 (Read question carefully, a task starts at si and finishes at si+ti-1, and at si+ti machine is free). Capacity=1, Cost= -Cost of edge.</p><p>Now it becomes mincost maxflow problem with max flow upto k. If u didnt get it then just above graph once for sample input. u will surely understand.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-591779 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-591779 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-591779\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1039946\" 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/nonrice\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2487084/avatar/f9f0266eade11795.jpg'/> </a>\n <div><a href=\"/profile/nonrice\" title=\"Expert nonrice\" class=\"rated-user user-blue\">nonrice</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/22/2023 19:35\">4 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1039946\" href=\"?#comment-1039946\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1039946\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2487084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1039946\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did reverse version (maximum to minimum) way in C-Range Increments using dsu</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1039946 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1039946 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1039946\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4327\" 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Robot Bicorn Attack"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Robot Bicorn Attack</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 Robot Bicorn Attack.</p><p>The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string <span class=\"tex-span\"><i>s</i></span>. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string <span class=\"tex-span\"><i>s</i></span>.</p><p>Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (<span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>) points for one round.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only line of input contains non-empty string <span class=\"tex-span\"><i>s</i></span> obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -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>1234<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>37<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>9000<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>90<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>0009<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 example the string must be split into numbers 1, 2 and 34.</p><p>In the second example the string must be split into numbers 90, 0 and 0. </p><p>In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes.</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=\"9431da0b4bb1ca182294e9a7671872c7\"/>\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=\"7236a5f2e4d7de224f73f0b21cda97e90d47e0df\"/>\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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resourceIds=\"964:965\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4353\" title=\"Codeforces Round #115 — editorial F\" target=\"_blank\">Tutorial #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"966:967\" resourceName=\"Tutorial #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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 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class=\"header\"><div class=\"title\">A. Robot Bicorn Attack</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 Robot Bicorn Attack.</p><p>The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string <span class=\"tex-span\"><i>s</i></span>. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string <span class=\"tex-span\"><i>s</i></span>.</p><p>Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (<span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>) points for one round.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only line of input contains non-empty string <span class=\"tex-span\"><i>s</i></span> obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -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>1234<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>37<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>9000<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>90<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>0009<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 example the string must be split into numbers 1, 2 and 34.</p><p>In the second example the string must be split into numbers 90, 0 and 0. </p><p>In the third example the string is incorrect, because after splitting the string 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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: 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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='6310623ffb5bb2dbb605f7f81999235e'/>\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/I_Remember_Olya_ashmelev\">I_Remember_Olya_ashmelev</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/I_Remember_Olya_ashmelev\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/I_Remember_Olya_ashmelev\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/I_Remember_Olya_ashmelev\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/I_Remember_Olya_ashmelev\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/I_Remember_Olya_ashmelev\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/I_Remember_Olya_ashmelev\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/I_Remember_Olya_ashmelev\" style=\"text-decoration:none;color:black !important;\">I_Remember_Olya_ashmelev'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=\"4353\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4339\"> <p>Codeforces Round #115 — editorial A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Plane of Tanks: Pro"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Plane of Tanks: Pro</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 has been playing Plane of Tanks with his friends the whole year. Now it is time to divide the participants into several categories depending on their results. </p><p>A player is given a non-negative integer number of points in each round of the Plane of Tanks. Vasya wrote results for each round of the last year. He has <span class=\"tex-span\"><i>n</i></span> records in total.</p><p>In order to determine a player's category consider the best result obtained by the player and the best results of other players. The player belongs to category: </p><ul> <li> \"<span class=\"tex-font-style-tt\">noob</span>\" — if <span class=\"tex-font-style-bf\">more than <span class=\"tex-span\">50%</span> of players have better results</span>; </li><li> \"<span class=\"tex-font-style-tt\">random</span>\" — if his result is not worse than the result that <span class=\"tex-span\">50%</span> of players have, but more than <span class=\"tex-span\">20%</span> of players have better results; </li><li> \"<span class=\"tex-font-style-tt\">average</span>\" — if his result is not worse than the result that <span class=\"tex-span\">80%</span> of players have, but more than <span class=\"tex-span\">10%</span> of players have better results; </li><li> \"<span class=\"tex-font-style-tt\">hardcore</span>\" — if his result is not worse than the result that <span class=\"tex-span\">90%</span> of players have, but more than <span class=\"tex-span\">1%</span> of players have better results; </li><li> \"<span class=\"tex-font-style-tt\">pro</span>\" — if his result is not worse than the result that <span class=\"tex-span\">99%</span> of players have. </li></ul> <p>When the percentage is calculated the player himself is taken into account. That means that if two players played the game and the first one gained 100 points and the second one 1000 points, then the first player's result is not worse than the result that <span class=\"tex-span\">50%</span> of players have, and the second one is not worse than the result that <span class=\"tex-span\">100%</span> of players have.</p><p>Vasya gave you the last year Plane of Tanks results. Help Vasya determine each player's category.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the only integer number <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1000</span>) — a number of records with the players' results.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains a player's name and the amount of points, obtained by the player for the round, separated with a space. The name contains not less than 1 and no more than 10 characters. The name consists of lowercase Latin letters only. It is guaranteed that any two different players have different names. The amount of points, obtained by the player for the round, is a non-negative integer number and does not exceed 1000.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print on the first line the number <span class=\"tex-span\"><i>m</i></span> — the number of players, who participated in one round at least.</p><p>Each one of the next <span class=\"tex-span\"><i>m</i></span> lines should contain a player name and a category he belongs to, separated with space. Category can be one of the following: \"<span class=\"tex-font-style-tt\">noob</span>\", \"<span class=\"tex-font-style-tt\">random</span>\", \"<span class=\"tex-font-style-tt\">average</span>\", \"<span class=\"tex-font-style-tt\">hardcore</span>\" or \"<span class=\"tex-font-style-tt\">pro</span>\" (without quotes). The name of each player should be printed only once. Player names with respective categories can be printed in an arbitrary order.</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/>vasya 100<br/>vasya 200<br/>artem 100<br/>kolya 200<br/>igor 250<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br/>artem noob<br/>igor pro<br/>kolya random<br/>vasya random<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>vasya 200<br/>kolya 1000<br/>vasya 1000<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>kolya pro<br/>vasya pro<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example the best result, obtained by <span class=\"tex-font-style-tt\">artem</span> is not worse than the result that <span class=\"tex-span\">25%</span> of players have (his own result), so he belongs to category \"<span class=\"tex-font-style-tt\">noob</span>\". <span class=\"tex-font-style-tt\">vasya</span> and <span class=\"tex-font-style-tt\">kolya</span> have best results not worse than the results that <span class=\"tex-span\">75%</span> players have (both of them and <span class=\"tex-font-style-tt\">artem</span>), so they belong to category \"<span class=\"tex-font-style-tt\">random</span>\". <span class=\"tex-font-style-tt\">igor</span> has best result not worse than the result that <span class=\"tex-span\">100%</span> of players have (all other players and himself), so he belongs to category \"<span class=\"tex-font-style-tt\">pro</span>\".</p><p>In the second example both players have the same amount of points, so they have results not worse than <span class=\"tex-span\">100%</span> players have, so they belong to category \"<span class=\"tex-font-style-tt\">pro</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=\"3646c1f715992c9759b75c1e1ad03fed\"/>\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=\"7236a5f2e4d7de224f73f0b21cda97e90d47e0df\"/>\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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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_cf5f9004ba6f5280ffa0e5233501d42070b54af3\">\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. Plane of Tanks: Pro</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 has been playing Plane of Tanks with his friends the whole year. Now it is time to divide the participants into several categories depending on their results. </p><p>A player is given a non-negative integer number of points in each round of the Plane of Tanks. Vasya wrote results for each round of the last year. He has <span class=\"tex-span\"><i>n</i></span> records in total.</p><p>In order to determine a player's category consider the best result obtained by the player and the best results of other players. The player belongs to category: </p><ul> <li> "<span class=\"tex-font-style-tt\">noob</span>" — if <span class=\"tex-font-style-bf\">more than <span class=\"tex-span\">50%</span> of players have better results</span>; </li><li> "<span class=\"tex-font-style-tt\">random</span>" — if his result is not worse than the result that <span class=\"tex-span\">50%</span> of players have, but more than <span class=\"tex-span\">20%</span> of players have better results; </li><li> "<span class=\"tex-font-style-tt\">average</span>" — if his result is not worse than the result that <span class=\"tex-span\">80%</span> of players have, but more than <span class=\"tex-span\">10%</span> of players have better results; </li><li> "<span class=\"tex-font-style-tt\">hardcore</span>" — if his result is not worse than the result that <span class=\"tex-span\">90%</span> of players have, but more than <span class=\"tex-span\">1%</span> of players have better results; </li><li> "<span class=\"tex-font-style-tt\">pro</span>" — if his result is not worse than the result that <span class=\"tex-span\">99%</span> of players have. </li></ul> <p>When the percentage is calculated the player himself is taken into account. That means that if two players played the game and the first one gained 100 points and the second one 1000 points, then the first player's result is not worse than the result that <span class=\"tex-span\">50%</span> of players have, and the second one is not worse than the result that <span class=\"tex-span\">100%</span> of players have.</p><p>Vasya gave you the last year Plane of Tanks results. Help Vasya determine each player's category.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the only integer number <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1000</span>) — a number of records with the players' results.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains a player's name and the amount of points, obtained by the player for the round, separated with a space. The name contains not less than 1 and no more than 10 characters. The name consists of lowercase Latin letters only. It is guaranteed that any two different players have different names. The amount of points, obtained by the player for the round, is a non-negative integer number and does not exceed 1000.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print on the first line the number <span class=\"tex-span\"><i>m</i></span> — the number of players, who participated in one round at least.</p><p>Each one of the next <span class=\"tex-span\"><i>m</i></span> lines should contain a player name and a category he belongs to, separated with space. Category can be one of the following: "<span class=\"tex-font-style-tt\">noob</span>", "<span class=\"tex-font-style-tt\">random</span>", "<span class=\"tex-font-style-tt\">average</span>", "<span class=\"tex-font-style-tt\">hardcore</span>" or "<span class=\"tex-font-style-tt\">pro</span>" (without quotes). The name of each player should be printed only once. Player names with respective categories can be printed in an arbitrary order.</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 />vasya 100<br />vasya 200<br />artem 100<br />kolya 200<br />igor 250<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br />artem noob<br />igor pro<br />kolya random<br />vasya random<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />vasya 200<br />kolya 1000<br />vasya 1000<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />kolya pro<br />vasya pro<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example the best result, obtained by <span class=\"tex-font-style-tt\">artem</span> is not worse than the result that <span class=\"tex-span\">25%</span> of players have (his own result), so he belongs to category "<span class=\"tex-font-style-tt\">noob</span>". <span class=\"tex-font-style-tt\">vasya</span> and <span class=\"tex-font-style-tt\">kolya</span> have best results not worse than the results that <span class=\"tex-span\">75%</span> players have (both of them and <span class=\"tex-font-style-tt\">artem</span>), so they belong to category "<span class=\"tex-font-style-tt\">random</span>". <span class=\"tex-font-style-tt\">igor</span> has best result not worse than the result that <span class=\"tex-span\">100%</span> of players have (all other players and himself), so he belongs to category "<span class=\"tex-font-style-tt\">pro</span>".</p><p>In the second example both players have the same amount of points, so they have results not worse than <span class=\"tex-span\">100%</span> players have, so they belong to category "<span class=\"tex-font-style-tt\">pro</span>".</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='6310623ffb5bb2dbb605f7f81999235e'/>\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)\" 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/I_Remember_Olya_ashmelev\">I_Remember_Olya_ashmelev</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/I_Remember_Olya_ashmelev\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/I_Remember_Olya_ashmelev\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/I_Remember_Olya_ashmelev\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/I_Remember_Olya_ashmelev\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/I_Remember_Olya_ashmelev\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/I_Remember_Olya_ashmelev\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/I_Remember_Olya_ashmelev\" style=\"text-decoration:none;color:black !important;\">I_Remember_Olya_ashmelev'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=\"4353\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4339\"> <p>Codeforces Round #115 — editorial A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Geometry Horse"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Geometry Horse</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 the Geometry Horse.</p><p>The game goal is to destroy geometric figures of the game world. A certain number of points is given for destroying each figure depending on the figure type and the current factor value. </p><p>There are <span class=\"tex-span\"><i>n</i></span> types of geometric figures. The number of figures of type <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> and figure cost <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> is known for each figure type. A player gets <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub>·<i>f</i> </span> points for destroying one figure of type <span class=\"tex-span\"><i>i</i></span>, where <span class=\"tex-span\"><i>f</i></span> is the current factor. The factor value can be an integer number from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>t</i> + 1</span>, inclusive. At the beginning of the game the factor value is equal to 1. The factor is set to <span class=\"tex-span\"><i>i</i> + 1</span> after destruction of <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ <i>t</i>)</span> figures, so the <span class=\"tex-span\">(<i>p</i><sub class=\"lower-index\"><i>i</i></sub> + 1)</span>-th figure to be destroyed is considered with factor equal to <span class=\"tex-span\"><i>i</i> + 1</span>.</p><p>Your task is to determine the maximum number of points Vasya can get after he destroys all figures. Take into account that Vasya is so tough that he can destroy figures in any order chosen by him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the only integer number <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 100)</span> — the number of figure types.</p><p>Each of the following <span class=\"tex-span\"><i>n</i></span> lines contains two integer numbers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup>, 0 ≤ <i>c</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 1000)</span>, separated with space — the number of figures of the <span class=\"tex-span\"><i>i</i></span>-th type and the cost of one <span class=\"tex-span\"><i>i</i></span>-type figure, correspondingly.</p><p>The next line contains the only integer number <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>t</i> ≤ 100)</span> — the number that describe the factor's changes. </p><p>The next line contains <span class=\"tex-span\"><i>t</i></span> integer numbers <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\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>t</i></sub> ≤ 10<sup class=\"upper-index\">12</sup>)</span>, separated with spaces.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specificator to read or write 64-bit integers in С++. It is preferred to use <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> specificator.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number — the maximum number of points Vasya can get.</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/>5 10<br/>2<br/>3 6<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>70</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br/>3 8<br/>5 10<br/>1<br/>20<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>74</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example Vasya destroys three figures first and gets <span class=\"tex-span\">3·1·10 = 30</span> points. Then the factor will become equal to <span class=\"tex-span\">2</span> and after destroying the last two figures Vasya will get <span class=\"tex-span\">2·2·10 = 40</span> points. As a result Vasya will get <span class=\"tex-span\">70</span> points.</p><p>In the second example all <span class=\"tex-span\">8</span> figures will be destroyed with factor <span class=\"tex-span\">1</span>, so Vasya will get <span class=\"tex-span\">(3·8 + 5·10)·1 = 74</span> points.</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=\"503a027d46159ca1d082fe998218e25a\"/>\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 - 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=\"7236a5f2e4d7de224f73f0b21cda97e90d47e0df\"/>\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/175\">Codeforces Round 115</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='503a027d46159ca1d082fe998218e25a'/>\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/175/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=\"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=\"Two pointers\">\r\n two pointers\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 *1600\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='503a027d46159ca1d082fe998218e25a'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1149\"/>\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='503a027d46159ca1d082fe998218e25a'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1149\"/>\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/4330\" title=\"Codeforces Round #115\" target=\"_blank\">Codeforces Round #115</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"384:385\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4339\" title=\"Codeforces Round #115 — editorial A-E\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"964:965\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4353\" title=\"Codeforces Round #115 — editorial F\" target=\"_blank\">Tutorial #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"966:967\" resourceName=\"Tutorial #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/175\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/175/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/175/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/175/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/175/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/175/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/175/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/175/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=\"C\" data-uuid=\"ps_eddbd38d5b4cfcd27fa877a1c4863bd1fb93c408\">\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. Geometry Horse</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 the Geometry Horse.</p><p>The game goal is to destroy geometric figures of the game world. A certain number of points is given for destroying each figure depending on the figure type and the current factor value. </p><p>There are <span class=\"tex-span\"><i>n</i></span> types of geometric figures. The number of figures of type <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> and figure cost <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> is known for each figure type. A player gets <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub>·<i>f</i> </span> points for destroying one figure of type <span class=\"tex-span\"><i>i</i></span>, where <span class=\"tex-span\"><i>f</i></span> is the current factor. The factor value can be an integer number from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>t</i> + 1</span>, inclusive. At the beginning of the game the factor value is equal to 1. The factor is set to <span class=\"tex-span\"><i>i</i> + 1</span> after destruction of <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ <i>t</i>)</span> figures, so the <span class=\"tex-span\">(<i>p</i><sub class=\"lower-index\"><i>i</i></sub> + 1)</span>-th figure to be destroyed is considered with factor equal to <span class=\"tex-span\"><i>i</i> + 1</span>.</p><p>Your task is to determine the maximum number of points Vasya can get after he destroys all figures. Take into account that Vasya is so tough that he can destroy figures in any order chosen by him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the only integer number <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 100)</span> — the number of figure types.</p><p>Each of the following <span class=\"tex-span\"><i>n</i></span> lines contains two integer numbers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup>, 0 ≤ <i>c</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 1000)</span>, separated with space — the number of figures of the <span class=\"tex-span\"><i>i</i></span>-th type and the cost of one <span class=\"tex-span\"><i>i</i></span>-type figure, correspondingly.</p><p>The next line contains the only integer number <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>t</i> ≤ 100)</span> — the number that describe the factor's changes. </p><p>The next line contains <span class=\"tex-span\"><i>t</i></span> integer numbers <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\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>t</i></sub> ≤ 10<sup class=\"upper-index\">12</sup>)</span>, separated with spaces.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specificator to read or write 64-bit integers in С++. It is preferred to use <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> specificator.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number — the maximum number of points Vasya can get.</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 />5 10<br />2<br />3 6<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>70</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br />3 8<br />5 10<br />1<br />20<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>74</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example Vasya destroys three figures first and gets <span class=\"tex-span\">3·1·10 = 30</span> points. Then the factor will become equal to <span class=\"tex-span\">2</span> and after destroying the last two figures Vasya will get <span class=\"tex-span\">2·2·10 = 40</span> points. As a result Vasya will get <span class=\"tex-span\">70</span> points.</p><p>In the second example all <span class=\"tex-span\">8</span> figures will be destroyed with factor <span class=\"tex-span\">1</span>, so Vasya will get <span class=\"tex-span\">(3·8 + 5·10)·1 = 74</span> points.</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 $problem.find(\".diff-notifier\").hide();\r\n });\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='6310623ffb5bb2dbb605f7f81999235e'/>\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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A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Plane of Tanks: Duel"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Plane of Tanks: Duel</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 the Plane of Tanks.</p><p>Tanks are described with the following attributes: </p><ul> <li> the number of hit points; </li><li> the interval between two gun shots (the time required to recharge the gun); </li><li> the probability that the gun shot will not pierce armor of the enemy tank; </li><li> the damage to the enemy's tank. </li></ul><p>The gun damage is described with a segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, where <span class=\"tex-span\"><i>l</i></span> and <span class=\"tex-span\"><i>r</i></span> are integer numbers. The potential gun damage <span class=\"tex-span\"><i>x</i></span> is chosen with equal probability among all integer numbers of the segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>. If the shot pierces the armor of an enemy's tank then the enemy loses <span class=\"tex-span\"><i>x</i></span> hit points. If the number of hit points becomes non-positive then the enemy tank is considered destroyed. </p><p>It is possible that the shot does not pierce the armor of a tank. In this case the number of hit points doesn't change. The probability that the armor will not be pierced is considered as the shooting tank attribute and does not depend on players' behavior.</p><p>The victory is near and there is only one enemy tank left. Vasya is ready for the battle — one more battle between the Good and the Evil is inevitable! Two enemies saw each other and each of them fired a shot at the same moment... The last battle has begun! Help Vasya to determine what is the probability that he will win the battle by destroying the enemy tank? </p><p>If both tanks are destroyed (after simultaneous shots), then Vasya is considered a winner. You can assume that each player fires a shot just after the gun recharge and each tank has infinite number of ammo.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains five integer numbers separated with spaces describing Vasya's tank: the number of hit points <span class=\"tex-span\"><i>hp</i></span> <span class=\"tex-span\">(10 ≤ <i>hp</i> ≤ 200)</span>, the interval between two shots <span class=\"tex-span\"><i>dt</i></span> <span class=\"tex-span\">(1 ≤ <i>dt</i> ≤ 30)</span>, gun damage segment <span class=\"tex-span\"><i>l</i></span> and <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(10 ≤ <i>l</i> ≤ <i>r</i> ≤ 100)</span>, the probability that the enemy's tank armor will not be pierced <span class=\"tex-span\"><i>p</i></span> <span class=\"tex-span\">(0 ≤ <i>p</i> ≤ 100)</span> (percents).</p><p>The second line describes the tank of Vasya's enemy in the same format.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number with absolute or relative error no more than <span class=\"tex-span\">10<sup class=\"upper-index\"> - 4</sup></span> — probability of Vasya's victory.</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>100 3 50 50 0<br/>100 3 50 50 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1.000000<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>100 3 50 50 0<br/>100 2 48 50 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.888889<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>100 3 50 50 0<br/>100 1 50 50 50<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.500000<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example both tanks are destroyed at once after the second shot. The probability of destroying the enemy tank is <span class=\"tex-span\">1</span>.</p><p>In the second example Vasya's enemy tank fires the second shot before Vasya's tank, but has no time for the third shot. In order to destroy Vasya's tank it is necessary to fire two shots with damage 50. The probability of that event is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5b8cbead818d4c86d1b85c58f6f83a955392b329.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> = <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3aa776870a184225f95e5a8de47bdeadf28fa805.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. Otherwise, Vasya wins.</p><p>In the third example Vasya's enemy tank fires three shots with probability of armor piercing <span class=\"tex-span\">0.5</span>. In order to destroy Vasya's tank it is necessary that at least 2 of 3 shots pierce the armor of Vasya's tank. 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data-uuid=\"ps_714b6d1ca69794df27733daa8d098abc508f77dc\">\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. Plane of Tanks: Duel</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 the Plane of Tanks.</p><p>Tanks are described with the following attributes: </p><ul> <li> the number of hit points; </li><li> the interval between two gun shots (the time required to recharge the gun); </li><li> the probability that the gun shot will not pierce armor of the enemy tank; </li><li> the damage to the enemy's tank. </li></ul><p>The gun damage is described with a segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, where <span class=\"tex-span\"><i>l</i></span> and <span class=\"tex-span\"><i>r</i></span> are integer numbers. The potential gun damage <span class=\"tex-span\"><i>x</i></span> is chosen with equal probability among all integer numbers of the segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>. If the shot pierces the armor of an enemy's tank then the enemy loses <span class=\"tex-span\"><i>x</i></span> hit points. If the number of hit points becomes non-positive then the enemy tank is considered destroyed. </p><p>It is possible that the shot does not pierce the armor of a tank. In this case the number of hit points doesn't change. The probability that the armor will not be pierced is considered as the shooting tank attribute and does not depend on players' behavior.</p><p>The victory is near and there is only one enemy tank left. Vasya is ready for the battle — one more battle between the Good and the Evil is inevitable! Two enemies saw each other and each of them fired a shot at the same moment... The last battle has begun! Help Vasya to determine what is the probability that he will win the battle by destroying the enemy tank? </p><p>If both tanks are destroyed (after simultaneous shots), then Vasya is considered a winner. You can assume that each player fires a shot just after the gun recharge and each tank has infinite number of ammo.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains five integer numbers separated with spaces describing Vasya's tank: the number of hit points <span class=\"tex-span\"><i>hp</i></span> <span class=\"tex-span\">(10 ≤ <i>hp</i> ≤ 200)</span>, the interval between two shots <span class=\"tex-span\"><i>dt</i></span> <span class=\"tex-span\">(1 ≤ <i>dt</i> ≤ 30)</span>, gun damage segment <span class=\"tex-span\"><i>l</i></span> and <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(10 ≤ <i>l</i> ≤ <i>r</i> ≤ 100)</span>, the probability that the enemy's tank armor will not be pierced <span class=\"tex-span\"><i>p</i></span> <span class=\"tex-span\">(0 ≤ <i>p</i> ≤ 100)</span> (percents).</p><p>The second line describes the tank of Vasya's enemy in the same format.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only number with absolute or relative error no more than <span class=\"tex-span\">10<sup class=\"upper-index\"> - 4</sup></span> — probability of Vasya's victory.</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>100 3 50 50 0<br />100 3 50 50 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1.000000<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>100 3 50 50 0<br />100 2 48 50 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.888889<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>100 3 50 50 0<br />100 1 50 50 50<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.500000<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first example both tanks are destroyed at once after the second shot. The probability of destroying the enemy tank is <span class=\"tex-span\">1</span>.</p><p>In the second example Vasya's enemy tank fires the second shot before Vasya's tank, but has no time for the third shot. In order to destroy Vasya's tank it is necessary to fire two shots with damage 50. The probability of that event is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5b8cbead818d4c86d1b85c58f6f83a955392b329.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> = <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3aa776870a184225f95e5a8de47bdeadf28fa805.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Otherwise, Vasya wins.</p><p>In the third example Vasya's enemy tank fires three shots with probability of armor piercing <span class=\"tex-span\">0.5</span>. In order to destroy Vasya's tank it is necessary that at least 2 of 3 shots pierce the armor of Vasya's tank. 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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='6310623ffb5bb2dbb605f7f81999235e'/>\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)\" 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/I_Remember_Olya_ashmelev\">I_Remember_Olya_ashmelev</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/I_Remember_Olya_ashmelev\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/I_Remember_Olya_ashmelev\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/I_Remember_Olya_ashmelev\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/I_Remember_Olya_ashmelev\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/I_Remember_Olya_ashmelev\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/I_Remember_Olya_ashmelev\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/I_Remember_Olya_ashmelev\" style=\"text-decoration:none;color:black !important;\">I_Remember_Olya_ashmelev'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=\"4353\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4339\"> <p>Codeforces Round #115 — editorial A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Power Defence"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Power Defence</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>Vasya plays the Power Defence. </p><p>He must pass the last level of the game. In order to do this he must kill the Main Villain, who moves in a straight line at speed 1 meter per second from the point <span class=\"tex-span\">( - ∞, 0)</span> to the point <span class=\"tex-span\">( + ∞, 0)</span> of the game world. In the points <span class=\"tex-span\">(<i>x</i>, 1)</span> and <span class=\"tex-span\">(<i>x</i>, - 1)</span>, where <span class=\"tex-span\"><i>x</i></span> is an integer number, Vasya can build towers of three types: fire-tower, electric-tower or freezing-tower. However, it is not allowed to build two towers at the same point. Towers of each type have a certain action radius and the value of damage per second (except freezing-tower). If at some point the Main Villain is in the range of action of <span class=\"tex-span\"><i>k</i></span> freezing towers then his speed is decreased by <span class=\"tex-span\"><i>k</i> + 1</span> times.</p><p>The allowed number of towers of each type is known. It is necessary to determine the maximum possible damage we can inflict on the Main Villain.</p><p>All distances in the problem are given in meters. The size of the Main Villain and the towers are so small, that they can be considered as points on the plane. The Main Villain is in the action radius of a tower if the distance between him and tower is less than or equal to the action radius of the tower.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains three integer numbers <span class=\"tex-span\"><i>nf</i>, <i>ne</i></span> and <span class=\"tex-span\"><i>ns</i></span> — the maximum number of fire-towers, electric-towers and freezing-towers that can be built <span class=\"tex-span\">(0 ≤ <i>nf</i>, <i>ne</i>, <i>ns</i> ≤ 20, 1 ≤ <i>nf</i> + <i>ne</i> + <i>ns</i> ≤ 20)</span>. The numbers are separated with single spaces.</p><p>The second line contains three integer numbers <span class=\"tex-span\"><i>rf</i>, <i>re</i></span> and <span class=\"tex-span\"><i>rs</i></span> <span class=\"tex-span\">(1 ≤ <i>rf</i>, <i>re</i>, <i>rs</i> ≤ 1000)</span> — the action radii of fire-towers, electric-towers and freezing-towers. The numbers are separated with single spaces.</p><p>The third line contains two integer numbers <span class=\"tex-span\"><i>df</i></span> and <span class=\"tex-span\"><i>de</i></span> <span class=\"tex-span\">(1 ≤ <i>df</i>, <i>de</i> ≤ 1000)</span> — the damage a fire-tower and an electronic-tower can inflict on the Main Villain per second (in the case when the Main Villain is in the action radius of the tower). The numbers are separated with single space.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only real number — the maximum possible damage to the Main Villain with absolute or relative error not more than <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>1 0 0<br/>10 10 10<br/>100 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1989.97487421</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 0 1<br/>10 10 10<br/>100 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3979.94974843</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample we've got one fire-tower that always inflicts the same damage, independently of its position. </p><p>In the second sample we've got another freezing-tower of the same action radius. If we build the two towers opposite each other, then the Main Villain's speed will be two times lower, whenever he enters the fire-tower's action radius. That means that the enemy will be inflicted with twice more damage.</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=\"2013447b61c8a78d661fe9d387e9e31b\"/>\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=\"7236a5f2e4d7de224f73f0b21cda97e90d47e0df\"/>\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/175\">Codeforces Round 115</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='2013447b61c8a78d661fe9d387e9e31b'/>\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/175/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=\"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=\"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=\"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=\"Difficulty\">\r\n *2600\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='2013447b61c8a78d661fe9d387e9e31b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1151\"/>\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='2013447b61c8a78d661fe9d387e9e31b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1151\"/>\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/4330\" title=\"Codeforces Round #115\" target=\"_blank\">Codeforces Round #115</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"384:385\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4339\" title=\"Codeforces Round #115 — editorial A-E\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"964:965\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4353\" title=\"Codeforces Round #115 — editorial F\" target=\"_blank\">Tutorial #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"966:967\" resourceName=\"Tutorial #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/175\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/175/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/175/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/175/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/175/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/175/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/175/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/175/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox 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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. Power Defence</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>Vasya plays the Power Defence. </p><p>He must pass the last level of the game. In order to do this he must kill the Main Villain, who moves in a straight line at speed 1 meter per second from the point <span class=\"tex-span\">( - ∞, 0)</span> to the point <span class=\"tex-span\">( + ∞, 0)</span> of the game world. In the points <span class=\"tex-span\">(<i>x</i>, 1)</span> and <span class=\"tex-span\">(<i>x</i>, - 1)</span>, where <span class=\"tex-span\"><i>x</i></span> is an integer number, Vasya can build towers of three types: fire-tower, electric-tower or freezing-tower. However, it is not allowed to build two towers at the same point. Towers of each type have a certain action radius and the value of damage per second (except freezing-tower). If at some point the Main Villain is in the range of action of <span class=\"tex-span\"><i>k</i></span> freezing towers then his speed is decreased by <span class=\"tex-span\"><i>k</i> + 1</span> times.</p><p>The allowed number of towers of each type is known. It is necessary to determine the maximum possible damage we can inflict on the Main Villain.</p><p>All distances in the problem are given in meters. The size of the Main Villain and the towers are so small, that they can be considered as points on the plane. The Main Villain is in the action radius of a tower if the distance between him and tower is less than or equal to the action radius of the tower.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains three integer numbers <span class=\"tex-span\"><i>nf</i>, <i>ne</i></span> and <span class=\"tex-span\"><i>ns</i></span> — the maximum number of fire-towers, electric-towers and freezing-towers that can be built <span class=\"tex-span\">(0 ≤ <i>nf</i>, <i>ne</i>, <i>ns</i> ≤ 20, 1 ≤ <i>nf</i> + <i>ne</i> + <i>ns</i> ≤ 20)</span>. The numbers are separated with single spaces.</p><p>The second line contains three integer numbers <span class=\"tex-span\"><i>rf</i>, <i>re</i></span> and <span class=\"tex-span\"><i>rs</i></span> <span class=\"tex-span\">(1 ≤ <i>rf</i>, <i>re</i>, <i>rs</i> ≤ 1000)</span> — the action radii of fire-towers, electric-towers and freezing-towers. The numbers are separated with single spaces.</p><p>The third line contains two integer numbers <span class=\"tex-span\"><i>df</i></span> and <span class=\"tex-span\"><i>de</i></span> <span class=\"tex-span\">(1 ≤ <i>df</i>, <i>de</i> ≤ 1000)</span> — the damage a fire-tower and an electronic-tower can inflict on the Main Villain per second (in the case when the Main Villain is in the action radius of the tower). The numbers are separated with single space.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the only real number — the maximum possible damage to the Main Villain with absolute or relative error not more than <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>1 0 0<br />10 10 10<br />100 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1989.97487421</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 0 1<br />10 10 10<br />100 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3979.94974843</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample we've got one fire-tower that always inflicts the same damage, independently of its position. </p><p>In the second sample we've got another freezing-tower of the same action radius. If we build the two towers opposite each other, then the Main Villain's speed will be two times lower, whenever he enters the fire-tower's action radius. That means that the enemy will be inflicted with twice more damage.</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 $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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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='6310623ffb5bb2dbb605f7f81999235e'/>\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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A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Gnomes of Might and Magic"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F. Gnomes of Might and Magic</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>8 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 popular game the Gnomes of Might and Magic.</p><p>In this game Vasya manages the kingdom of gnomes, consisting of several castles, connected by bidirectional roads. The kingdom road network has a special form. The kingdom has <span class=\"tex-span\"><i>m</i></span> main castles <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span>, which form the Good Path. This path consists of roads between the castles <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></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>m</i>)</span> as well as the road between <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. There are no other roads between the castles of the Good Path.</p><p>In addition, for each pair of neighboring Good Path castles <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>v</i></span> there is exactly one Evil Shortcut — a path that goes along the roads leading from the first castle <span class=\"tex-span\">(<i>u</i>)</span> to the second one <span class=\"tex-span\">(<i>v</i>)</span> and not having any common vertexes with the Good Path except for the vertexes <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>v</i></span>. It is known that there are no other roads and castles in the kingdom there, that is, every road and every castle lies either on the Good Path or the Evil Shortcut (castles can lie in both of them). In addition, no two Evil Shortcuts have any common castles, different than the castles of the Good Path.</p><p>At the beginning of each week in the kingdom appears one very bad gnome who stands on one of the roads of the kingdom, and begins to rob the corovans going through this road. One road may accumulate multiple very bad gnomes. Vasya cares about his corovans, so sometimes he sends the Mission of Death from one castle to another.</p><p>Let's suggest that the Mission of Death should get from castle <span class=\"tex-span\"><i>s</i></span> to castle <span class=\"tex-span\"><i>t</i></span>. Then it will move from castle <span class=\"tex-span\"><i>s</i></span> to castle <span class=\"tex-span\"><i>t</i></span>, destroying all very bad gnomes, which are on the roads of the Mission's path. Vasya is so tough that his Mission of Death can destroy any number of gnomes on its way. However, Vasya is very kind, so he always chooses such path between castles <span class=\"tex-span\"><i>s</i></span> and <span class=\"tex-span\"><i>t</i></span>, following which he will destroy the smallest number of gnomes. If there are multiple such paths, then Vasya chooses the path that contains the smallest number of roads among them. If there are multiple such paths still, Vasya chooses the lexicographically minimal one among them.</p><p>Help Vasya to simulate the life of the kingdom in the Gnomes of Might and Magic game.</p><p>A path is a sequence of castles, such that each pair of the neighboring castles on the path is connected by a road. Also, path <span class=\"tex-span\"><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>p</i></sub></span> is lexicographically less than path <span class=\"tex-span\"><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>q</i></sub></span>, if either <span class=\"tex-span\"><i>p</i> < <i>q</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>p</i></sub> = <i>y</i><sub class=\"lower-index\"><i>p</i></sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < <i>p</i>, <i>r</i> < <i>q</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>.</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\">(3 ≤ <i>m</i> ≤ <i>n</i> ≤ 100000)</span> — the number of castles in the kingdom, and the number of castles on the Good Path, respectively.</p><p>The second line contains <span class=\"tex-span\"><i>m</i></span> integers, which are numbers of Good Path castles (the castles are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>) in the order of occurrence on the Path, starting with some castle. All Good Path castles are different.</p><p>Each of the following <span class=\"tex-span\"><i>m</i></span> lines describes an Evil Shortcut. First a line contains an integer <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(3 ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100000)</span> — the number of castles on the corresponding Evil Shortcut (with the two castles which are on the Good Path), followed by a <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> integers — number of castles in the order of occurrence in the given Shortcut. All castles in one Evil Shortcut are different. It is guaranteed that the first and the last castles from the Shortcut are on the Good Path and the first castles in the Evil Shortcuts form the Good Path and are presented in the same order in which the Path was represented on the second line.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> <span class=\"tex-span\">(1 ≤ <i>q</i> ≤ 100000)</span> — the number of events in the life of the kingdom. Each of the following <span class=\"tex-span\"><i>q</i></span> lines describes a single event. An event is described by the symbol <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> and two numbers or castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span> (the character and numbers of castles are separated by a single space). If the character of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> is equal to \"<span class=\"tex-font-style-tt\">+</span>\" (a plus), it means that a very bad gnome (probably not the first one) has appeared on the road between castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>. If <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> equals \"<span class=\"tex-font-style-tt\">?</span>\" (a question), then Vasya sent a Mission of Death from castle <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> to castle <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>. It is guaranteed that for each request \"<span class=\"tex-font-style-tt\">+</span>\", the road between castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span> exists. The events are given in chronological order, starting with the earliest one. Initially there are no very bad gnomes on the roads.</p><p>All numbers in all lines are separated by single spaces. It is guaranteed that all the given Evil Shortcuts and Good Path fit in the limitations given in the problem statement.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each query \"<span class=\"tex-font-style-tt\">?</span>\" print a single number on a single line — the number of very bad gnomes destroyed by the corresponding Mission of Death. Print the answers to queries in the chronological order.</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 3<br/>1 2 3<br/>3 1 4 2<br/>3 2 5 3<br/>3 3 6 1<br/>10<br/>+ 1 2<br/>+ 4 2<br/>+ 1 3<br/>+ 2 3<br/>? 1 2<br/>+ 2 5<br/>? 1 2<br/>? 1 2<br/>+ 1 2<br/>? 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/>1<br/>0<br/>1<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the example after the first four requests there is only one path from castle 1 to castle 2, which does not contain roads with very bad gnomes: 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 6 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 3 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 5 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 2.</p><p>After a gnome stood on the road (2, 5), the next Mission of Death moves along path 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 2, and destroys the gnome, who was on the road (1, 2). The next Mission of Death follows the same path which is already free of gnomes.</p><p>After yet another gnome stood on the road (1, 2), the next Mission of Death goes on the path 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> 2, and kills the gnome.</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=\"cbef161ba295d08ec017206929d1dc74\"/>\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 - F - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"7236a5f2e4d7de224f73f0b21cda97e90d47e0df\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F - 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/175\">Codeforces Round 115</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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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 *3000\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='cbef161ba295d08ec017206929d1dc74'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1152\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" 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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=\"F\" data-uuid=\"ps_aafe54bc0ef8719263035365e6068eaacff8ba78\">\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\">F. Gnomes of Might and Magic</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>8 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 popular game the Gnomes of Might and Magic.</p><p>In this game Vasya manages the kingdom of gnomes, consisting of several castles, connected by bidirectional roads. The kingdom road network has a special form. The kingdom has <span class=\"tex-span\"><i>m</i></span> main castles <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span>, which form the Good Path. This path consists of roads between the castles <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></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>m</i>)</span> as well as the road between <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. There are no other roads between the castles of the Good Path.</p><p>In addition, for each pair of neighboring Good Path castles <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>v</i></span> there is exactly one Evil Shortcut — a path that goes along the roads leading from the first castle <span class=\"tex-span\">(<i>u</i>)</span> to the second one <span class=\"tex-span\">(<i>v</i>)</span> and not having any common vertexes with the Good Path except for the vertexes <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>v</i></span>. It is known that there are no other roads and castles in the kingdom there, that is, every road and every castle lies either on the Good Path or the Evil Shortcut (castles can lie in both of them). In addition, no two Evil Shortcuts have any common castles, different than the castles of the Good Path.</p><p>At the beginning of each week in the kingdom appears one very bad gnome who stands on one of the roads of the kingdom, and begins to rob the corovans going through this road. One road may accumulate multiple very bad gnomes. Vasya cares about his corovans, so sometimes he sends the Mission of Death from one castle to another.</p><p>Let's suggest that the Mission of Death should get from castle <span class=\"tex-span\"><i>s</i></span> to castle <span class=\"tex-span\"><i>t</i></span>. Then it will move from castle <span class=\"tex-span\"><i>s</i></span> to castle <span class=\"tex-span\"><i>t</i></span>, destroying all very bad gnomes, which are on the roads of the Mission's path. Vasya is so tough that his Mission of Death can destroy any number of gnomes on its way. However, Vasya is very kind, so he always chooses such path between castles <span class=\"tex-span\"><i>s</i></span> and <span class=\"tex-span\"><i>t</i></span>, following which he will destroy the smallest number of gnomes. If there are multiple such paths, then Vasya chooses the path that contains the smallest number of roads among them. If there are multiple such paths still, Vasya chooses the lexicographically minimal one among them.</p><p>Help Vasya to simulate the life of the kingdom in the Gnomes of Might and Magic game.</p><p>A path is a sequence of castles, such that each pair of the neighboring castles on the path is connected by a road. Also, path <span class=\"tex-span\"><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>p</i></sub></span> is lexicographically less than path <span class=\"tex-span\"><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>q</i></sub></span>, if either <span class=\"tex-span\"><i>p</i> < <i>q</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>p</i></sub> = <i>y</i><sub class=\"lower-index\"><i>p</i></sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < <i>p</i>, <i>r</i> < <i>q</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>.</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\">(3 ≤ <i>m</i> ≤ <i>n</i> ≤ 100000)</span> — the number of castles in the kingdom, and the number of castles on the Good Path, respectively.</p><p>The second line contains <span class=\"tex-span\"><i>m</i></span> integers, which are numbers of Good Path castles (the castles are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>) in the order of occurrence on the Path, starting with some castle. All Good Path castles are different.</p><p>Each of the following <span class=\"tex-span\"><i>m</i></span> lines describes an Evil Shortcut. First a line contains an integer <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(3 ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100000)</span> — the number of castles on the corresponding Evil Shortcut (with the two castles which are on the Good Path), followed by a <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> integers — number of castles in the order of occurrence in the given Shortcut. All castles in one Evil Shortcut are different. It is guaranteed that the first and the last castles from the Shortcut are on the Good Path and the first castles in the Evil Shortcuts form the Good Path and are presented in the same order in which the Path was represented on the second line.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> <span class=\"tex-span\">(1 ≤ <i>q</i> ≤ 100000)</span> — the number of events in the life of the kingdom. Each of the following <span class=\"tex-span\"><i>q</i></span> lines describes a single event. An event is described by the symbol <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> and two numbers or castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span> (the character and numbers of castles are separated by a single space). If the character of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> is equal to "<span class=\"tex-font-style-tt\">+</span>" (a plus), it means that a very bad gnome (probably not the first one) has appeared on the road between castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>. If <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>j</i></sub></span> equals "<span class=\"tex-font-style-tt\">?</span>" (a question), then Vasya sent a Mission of Death from castle <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> to castle <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span>. It is guaranteed that for each request "<span class=\"tex-font-style-tt\">+</span>", the road between castles <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>j</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>j</i></sub></span> exists. The events are given in chronological order, starting with the earliest one. Initially there are no very bad gnomes on the roads.</p><p>All numbers in all lines are separated by single spaces. It is guaranteed that all the given Evil Shortcuts and Good Path fit in the limitations given in the problem statement.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each query "<span class=\"tex-font-style-tt\">?</span>" print a single number on a single line — the number of very bad gnomes destroyed by the corresponding Mission of Death. Print the answers to queries in the chronological order.</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 3<br />1 2 3<br />3 1 4 2<br />3 2 5 3<br />3 3 6 1<br />10<br />+ 1 2<br />+ 4 2<br />+ 1 3<br />+ 2 3<br />? 1 2<br />+ 2 5<br />? 1 2<br />? 1 2<br />+ 1 2<br />? 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br />1<br />0<br />1<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the example after the first four requests there is only one path from castle 1 to castle 2, which does not contain roads with very bad gnomes: 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 6 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 3 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 5 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 2.</p><p>After a gnome stood on the road (2, 5), the next Mission of Death moves along path 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 2, and destroys the gnome, who was on the road (1, 2). The next Mission of Death follows the same path which is already free of gnomes.</p><p>After yet another gnome stood on the road (1, 2), the next Mission of Death goes on the path 1 <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> 2, and kills the gnome.</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=F]\");\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, 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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='6310623ffb5bb2dbb605f7f81999235e'/>\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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A-E</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a>,\r\n <span class=\"format-humantime\" title=\"Apr/15/2012 07:08\">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 href=\"/contest/175/problem/A\" title=\"Codeforces Round 115\">175A - Robot Bicorn Attack</a></h4><p>Go over all possible partitions of the given string into 3 substrings (for example, go over a pair of indexes — the ends of the first and the second substrings). If all three substrings of the partition satisfy constraints (there are no leading zeroes and the corresponding number does not exceed 1000000), then update the current answer with the sum of obtained numbers (if it is necessary). The total amount of partitions is <em>O(N^2)</em>, where <em>N</em> is the length of the string. The check of one partition takes <em>O(N)</em>.</p><h4>Problem <a href=\"/contest/175/problem/B\" title=\"Codeforces Round 115\">175B - Plane of Tanks: Pro</a></h4><p>The solution is to simulate actions described in the statement. Find the best result for each player and count total amount of players <em>N</em>. Then find a number of players <em>C</em> for each player , those results are not better than best result of the considering player (this can be done by going over all players). Then it is necessary to determine players category using numbers <em>C</em> and <em>N</em>. In order to avoid rounding error use the following approach:</p> <ul> <li>if <em>C</em> * 100 >= <em>N</em> * 99, then the player belongs to category "pro"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 90, then the player is "hardcore"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 80, then the player is "average"</li> <li>if <em>C</em> * 100 >= <em>N</em> * 50, then the player is "random"</li> </ul><p>In other case the player is "noob".</p><h4>Problem <a href=\"/contest/175/problem/C\" title=\"Codeforces Round 115\">175C - Geometry Horse</a></h4><p>Obvious, that figures should be destroyed in the cost increasing order. Sort figures type in ascending order of their costs. Consider two pointers – position <em>i</em> in the array <em>P</em> (current factor) and position <em>j</em> in the array of figures type. Consider the current answer and the number of figures <em>G</em>, those need to be destroyed to move to the next value of factor. If the number of figures <em>F</em> of the current type does not exceed <em>G</em>, then add <em>F * (i + 1) * Сj</em> to the answer and reduce <em>G</em> by <em>F</em> and increase pointer <em>j</em> by 1. In other case add <em>G * (i + 1) * Cj</em> to the answer, reduce <em>F</em> by <em>G</em>, increase <em>i</em> by 1 and set <em>G = Pi – P(i-1)</em>. Continue iteration until all figure types are considered.</p><h4>Problem <a href=\"/contest/175/problem/D\" title=\"Codeforces Round 115\">175D - Plane of Tanks: Duel</a></h4><p>First consider case when at least one probability of not-piercing is equal to 100%. If Vasya does not pierce the enemy tank with probability 100%, then the answer is 0. If the enemy tank cannot pierce Vasya's tank with probability 100% then the answer is 1. Then consider that the probability of shot does not pierce tank does not exceed 99%. It can be checked that the probability that tank will stay alive after <em>D</em> = 5000 shots is less than 10^-6 (for any damage value, probability of not-piercing and amount of hit points). For each tank calculate the following table <em>dp</em>[<em>i</em>][<em>j</em>] — probability that tank will have <em>j</em> hit points after i shots to him. <em>dp</em>[0][<em>hp</em>] = 1, where <em>hp</em> – is the initial amount of hit points. In order to calculate the line <em>dp</em>[<em>i+1</em>] it is necessary to go over all possible damages for each value of <em>j</em> in the line <em>dp</em>[<em>i</em>], which shot <em>(i+1)</em>-th damages (considering cases when the shot does not pierce the tank armour) and update appropriate values of the line <em>(i+1)</em>:</p> <pre><code>dp[i + 1][max(0, j – x)] += dp[i][j] * (1 – p) / (r – l + 1)\n</code></pre><p>where <em>p</em> – is the probability of not-piercing, <em>x</em> – possible shot damage. Let's <em>dpv</em> – calculcated table for Vasya's tank and <em>dpe</em> is the table for enemy's tank. Now it is necessary to find probability that enemy's tank will be destroyed after <em>i</em> shots of Vasya's tank: <em>pk</em>[<em>i</em>] = <em>dpe</em>[<em>i</em>][0] – <em>dpe</em>[<em>i-1</em>][0]. Vasya wins the following way: Vasya fired <em>(K — 1)</em> shots and do not destroy enemy tank and is still alive also. After that Vasya fires <em>K</em>-th shot and destroy the enemy. Go over <em>K</em> and calculate the probability of Vasya's victory with the <em>K</em>-th shot. In order to do this find how many shots <em>T</em> can fire the enemy before Vasya makes <em>K</em>-th shot (here is the only place in the solution where we must use the gun recharge speed): </p> <pre><code>T = ((K – 1) * dtv + dte - 1) / dte\n</code></pre><p>where <em>dtv</em> is the time required to recharge the gun, <em>dte</em> is the time of enemy gun recharge. Then the probability of victory is (1 – <em>dpv</em>[<em>T</em>][0]) * <em>pk</em>[<em>K</em>]. The answer for the problem is the sum all these probabilities for each <em>K</em> from 1 to <em>D</em>. The algorithmic complexity of the algorithm is <em>O(D * hp * (r – l))</em>.</p><h4>Задача <a href=\"/contest/175/problem/E\" title=\"Codeforces Round 115\">175E - Power Defence</a></h4><p>If we reflect the position of towers alogn the line OX then the interval where towers will affect the Villain will not change. So, we can consider that towers can be built in the points (_x_, 1), not more than two towers in the same point. If there exists point <em>X</em> that there are towers to the left and to the right from <em>X</em> but in the point <em>X</em> there is no tower, then abscissas of all towers "to the right" can be reduced by 1 and the answer will not become worse. The same way, we can prove that there are no adjacent points with exactly one tower in each one. Now it is easy to check that in order to construct the optimal solution it is enough to check 13 successive points. </p><p>Go over positions of freezing towers. In the worst case there are approximately 200000 cases to put freezing towers into 13 points. Consider the case when we fixed positions of several freezing towers. Let's calculate how much damage can hit fire-tower or electric-tower in the point for each empty points (points where we can put two towers are splitted into two) and save numbers into the array <em>d</em> (_d_[<em>k</em>].f and <em>d</em>[<em>k</em>].e – damage by fire and electricity in the point <em>k</em> correspondingly). Sort the array <em>d</em> in the order of decreasing of the value <em>d</em>[<em>k</em>].f. Then optimal position of the rest towers can be found using dynamic programming. Designate <em>dp</em>[<em>i</em>][<em>j</em>] – the maximum possible damage, which can be hitted if we have <em>i</em> fire-towers and <em>j</em> electric-towers. Designate <em>p</em> — the amount of towers have been set already: <em>p = cf – i + ce – j</em>. If <em>i</em> = 0 then we used first <em>p</em> values of array <em>d</em> and the answer is the sum of <em>j</em> maximum elemets of <em>d</em>[<em>k</em>].e, starting from index <em>p</em>. Otherwise we put one fire-tower or one electric tower in the position <em>p</em>. It is necessary to put the tower into position <em>p</em> because in the opposite case the <em>d</em>[<em>p</em>].f will decrease. Then:</p> <pre><code>dp[i][j] += max(dp[i - 1][j] + d[p].f, d[i][j – 1] + d[p].e)\n</code></pre><p>The answer is the value <em>dp</em>[<em>cf</em>][<em>ce</em>], which is calculated in <em>O(cf * ce * log(ce))</em></p><p><strong>Comment1</strong>: exhaustive search can be reduced in 2 times because any two symmetric towers arrangements are equivalent and have the same answer. However, this optimization is not required with a given constraints.</p><p><strong>Comment2</strong>: the formula of Villain speed decrease <em>1 / (K + 1)</em> allows to calculate the tower damage for a case when all freezing towers are fixed easily. Freezing towers can be taken into account separately.</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/175\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 115</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-368-4353\").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: \"368\",\n blogEntryId: \"4339\",\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=round+115\" class=\"tag notice\" style=\"text-decoration: none;\">round 115</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-4353\"><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'>+23</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4353\"><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/I_Remember_Olya_ashmelev\"><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/I_Remember_Olya_ashmelev\">\n I_Remember_Olya_ashmelev\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=\"Apr/15/2012 07:08\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4339#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/4339#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=\"4363\">\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 (6)</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=\"88268\" 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/cherudim\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/25704/avatar/697bcaedc1a7af08.jpg'/> </a>\n <div><a href=\"/profile/cherudim\" title=\"Master cherudim\" class=\"rated-user user-orange\">cherudim</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 10:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88268\" href=\"?#comment-88268\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88268\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"9\"\r\n data-commentUserId=\"25704\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+9</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88268\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>THX!But how can I find solution to F?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88268 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88268 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88268\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88331\" commentParentId=\"88268\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dj3500\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6060/avatar/9a7b6f67e564c6b6.jpg'/> </a>\n <div><a href=\"/profile/dj3500\" title=\"Grandmaster dj3500\" class=\"rated-user user-red\">dj3500</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/17/2012 23:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88331\" href=\"?#comment-88331\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88268\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88331\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"6060\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88331\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe it's still an open problem ;)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88331 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88331 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88331\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"89299\" commentParentId=\"88331\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/I_Remember_Olya_ashmelev\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/577/avatar/c4603e9bec842bd0.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/I_Remember_Olya_ashmelev\" title=\"Grandmaster I_Remember_Olya_ashmelev\" class=\"rated-user user-red\">I_Remember_Olya_ashmelev</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/24/2012 17:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-89299\" href=\"?#comment-89299\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88331\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"89299\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"577\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-89299\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/blog/entry/4353\">Editorial</a> is published. Sorry for the delay.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-89299 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-89299 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-89299\">\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=\"88959\" 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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 09:15\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88959\" href=\"?#comment-88959\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88959\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88959\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Are there anyone who are kind enough to translate this image into English? <img alt=\" \" src=\"https://lh3.googleusercontent.com/-3800hg7BqM4/T4o-RaVXNrI/AAAAAAAAA2w/RrvyI5fD4pw/s720/pro.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>This image was posted to the Russian version of this article.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88959 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88959 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88959\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88964\" commentParentId=\"88959\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ItsLastDay\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6489/avatar/c3d65218855c3c7a.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/ItsLastDay\" title=\"Expert ItsLastDay\" class=\"rated-user user-blue\">ItsLastDay</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 10:11\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88964\" href=\"?#comment-88964\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88959\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88964\" 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=\"88964\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"10\"\r\n data-commentUserId=\"6489\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88964\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>1) noob "this game is quite nice and people are so kind"</li> <li>2) random player "we've lost, but I had so much fun!"</li> <li>3) avrerage player "We've lost again... But, undoubtedly, we will win next round!"</li> <li>4) hardcore player "OMG THIS TEAM SUCKS, DOES ANYONE OF YOU KNOW HOW TO PLAY?"</li> <li>5) Pro</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88964 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88964 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88964\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88991\" commentParentId=\"88964\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/mikeCAT\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/51461/avatar/63c88f6b6ed241df.jpg'/> </a>\n <div><a href=\"/profile/mikeCAT\" title=\"Master mikeCAT\" class=\"rated-user user-orange\">mikeCAT</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 13:19\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88991\" href=\"?#comment-88991\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88964\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88991\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"51461\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88991\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you very much! Now, I can understand what they say!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88991 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88991 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88991\">\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-4363\" 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\" 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Trading Business"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Trading Business</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>To get money for a new aeonic blaster, ranger Qwerty decided to engage in trade for a while. He wants to buy some number of items (or probably not to buy anything at all) on one of the planets, and then sell the bought items on another planet. Note that this operation is not repeated, that is, the buying and the selling are made only once. To carry out his plan, Qwerty is going to take a bank loan that covers all expenses and to return the loaned money at the end of the operation (the money is returned without the interest). At the same time, Querty wants to get as much profit as possible.</p><p>The system has <span class=\"tex-span\"><i>n</i></span> planets in total. On each of them Qwerty can buy or sell items of <span class=\"tex-span\"><i>m</i></span> types (such as food, medicine, weapons, alcohol, and so on). For each planet <span class=\"tex-span\"><i>i</i></span> and each type of items <span class=\"tex-span\"><i>j</i></span> Qwerty knows the following:</p><ul><li> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the cost of buying an item; </li><li> <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the cost of selling an item; </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the number of remaining items.</li></ul><p>It is not allowed to buy more than <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> items of type <span class=\"tex-span\"><i>j</i></span> on planet <span class=\"tex-span\"><i>i</i></span>, but it is allowed to sell any number of items of any kind.</p><p>Knowing that the hold of Qwerty's ship has room for no more than <span class=\"tex-span\"><i>k</i></span> items, determine the maximum profit which Qwerty can get.</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>n</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10</span>, <span class=\"tex-span\">1 ≤ <i>m</i>, <i>k</i> ≤ 100</span>) — the number of planets, the number of question types and the capacity of Qwerty's ship hold, correspondingly.</p><p>Then follow <span class=\"tex-span\"><i>n</i></span> blocks describing each planet.</p><p>The first line of the <span class=\"tex-span\"><i>i</i></span>-th block has the planet's name as a string with length from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">10</span> Latin letters. The first letter of the name is uppercase, the rest are lowercase. Then in the <span class=\"tex-span\"><i>i</i></span>-th block follow <span class=\"tex-span\"><i>m</i></span> lines, the <span class=\"tex-span\"><i>j</i></span>-th of them contains three integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>ij</i></sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>ij</i></sub> < <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1000</span>, <span class=\"tex-span\">0 ≤ <i>c</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100</span>) — the numbers that describe money operations with the <span class=\"tex-span\"><i>j</i></span>-th item on the <span class=\"tex-span\"><i>i</i></span>-th planet. The numbers in the lines are separated by spaces.</p><p>It is guaranteed that the names of all planets are different.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum profit Qwerty can get.</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 10<br/>Venus<br/>6 5 3<br/>7 6 5<br/>8 6 10<br/>Earth<br/>10 9 0<br/>8 6 4<br/>10 9 3<br/>Mars<br/>4 3 0<br/>8 4 12<br/>7 2 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>16</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first test case you should fly to planet <span class=\"tex-font-style-tt\">Venus</span>, take a loan on 74 units of money and buy three items of the first type and 7 items of the third type (<span class=\"tex-span\">3·6 + 7·8 = 74</span>). Then the ranger should fly to planet <span class=\"tex-font-style-tt\">Earth</span> and sell there all the items he has bought. He gets <span class=\"tex-span\">3·9 + 7·9 = 90</span> units of money for the items, he should give 74 of them for the loan. The resulting profit equals 16 units of money. 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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=\"A\" data-uuid=\"ps_cefcd6309155c1e438103ac112ee42f9426520a7\">\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. Trading Business</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>To get money for a new aeonic blaster, ranger Qwerty decided to engage in trade for a while. He wants to buy some number of items (or probably not to buy anything at all) on one of the planets, and then sell the bought items on another planet. Note that this operation is not repeated, that is, the buying and the selling are made only once. To carry out his plan, Qwerty is going to take a bank loan that covers all expenses and to return the loaned money at the end of the operation (the money is returned without the interest). At the same time, Querty wants to get as much profit as possible.</p><p>The system has <span class=\"tex-span\"><i>n</i></span> planets in total. On each of them Qwerty can buy or sell items of <span class=\"tex-span\"><i>m</i></span> types (such as food, medicine, weapons, alcohol, and so on). For each planet <span class=\"tex-span\"><i>i</i></span> and each type of items <span class=\"tex-span\"><i>j</i></span> Qwerty knows the following:</p><ul><li> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the cost of buying an item; </li><li> <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the cost of selling an item; </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> — the number of remaining items.</li></ul><p>It is not allowed to buy more than <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> items of type <span class=\"tex-span\"><i>j</i></span> on planet <span class=\"tex-span\"><i>i</i></span>, but it is allowed to sell any number of items of any kind.</p><p>Knowing that the hold of Qwerty's ship has room for no more than <span class=\"tex-span\"><i>k</i></span> items, determine the maximum profit which Qwerty can get.</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>n</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10</span>, <span class=\"tex-span\">1 ≤ <i>m</i>, <i>k</i> ≤ 100</span>) — the number of planets, the number of question types and the capacity of Qwerty's ship hold, correspondingly.</p><p>Then follow <span class=\"tex-span\"><i>n</i></span> blocks describing each planet.</p><p>The first line of the <span class=\"tex-span\"><i>i</i></span>-th block has the planet's name as a string with length from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">10</span> Latin letters. The first letter of the name is uppercase, the rest are lowercase. Then in the <span class=\"tex-span\"><i>i</i></span>-th block follow <span class=\"tex-span\"><i>m</i></span> lines, the <span class=\"tex-span\"><i>j</i></span>-th of them contains three integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>ij</i></sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>ij</i></sub> < <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1000</span>, <span class=\"tex-span\">0 ≤ <i>c</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100</span>) — the numbers that describe money operations with the <span class=\"tex-span\"><i>j</i></span>-th item on the <span class=\"tex-span\"><i>i</i></span>-th planet. The numbers in the lines are separated by spaces.</p><p>It is guaranteed that the names of all planets are different.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum profit Qwerty can get.</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 10<br />Venus<br />6 5 3<br />7 6 5<br />8 6 10<br />Earth<br />10 9 0<br />8 6 4<br />10 9 3<br />Mars<br />4 3 0<br />8 4 12<br />7 2 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>16</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first test case you should fly to planet <span class=\"tex-font-style-tt\">Venus</span>, take a loan on 74 units of money and buy three items of the first type and 7 items of the third type (<span class=\"tex-span\">3·6 + 7·8 = 74</span>). Then the ranger should fly to planet <span class=\"tex-font-style-tt\">Earth</span> and sell there all the items he has bought. He gets <span class=\"tex-span\">3·9 + 7·9 = 90</span> units of money for the items, he should give 74 of them for the loan. The resulting profit equals 16 units of money. 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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=''>13:54:57</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='15679b166c86ee80065b195f1dc12b4b'/>\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=\"4386\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4372\"> <p>Croc Champ 2012 — Round 2 — Editorial</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=\"Apr/20/2012 19:48\">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>A div2.</strong> Required row is row that have only one star inside. Requred column is comumn that also have only one star inside. So, you can iterate over all rows/columns, calculate number of stars inside them and find the answer.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B div2.</strong> Naive solution <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> (where you check all triplets) doesn't fin into time limits.</p><p>You can see that for every two points from triplet (for example, for A and C) you can find place of the third point. So you can find number of requred triplets just inerate over all pairs of points and check middle point between points in every pair.</p><p>How to fast check position? You can add 1000 for all coordinates (you can see that this operation doesn't change the answer) and mark them in the 2-dimensional boolean array 2001х2001. So you can check every position for point in <span class=\"tex-span\"><i>O</i>(1)</span> time.</p><p>Obtained solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a></p><p><strong>A div1. C div2.</strong> In this problem some greedy solution expected.</p><p>Let fix 2 planets: in planet i we will buy items, in planet j we will sell the ones. <em>Profit of item</em> of type k will be b_jk-a_ik. Every item has size 1, so you should greedy take items in order of decreasing of profits of items while you have place in the hold.</p><p>Scheme of full solution: you should iterate over all pairs of planet, for every pair greedy take items and find total profit. At the end you should find maximal total profit over all pairs and output it.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>B div1. D div2.</strong> You can see that split oparetion is just cyclically shift of string. You can go from any cyclically shift to any other one except the current one.</p><p>Let's call some cyclically shift <em>good</em> iff it equal to the final string. All others cyclically shifts we will call <em>bad</em>. You can check all shifts in <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup>)</span> time. Let's you have A good shifts and B bad ones.</p><p>Let's define dpA[n] as number of ways to get some good shift using n splits and за dpB[n] as number of ways to get some bad shift using n splits.</p><p>dpA[0]=1, dpB[0]=0 or dpA[0]=0, dpB[0]=1 according to the first shift is good or not. All other values of dp you can get using following reccurences:</p><p>dpA[n] = dpA[n-1] * (A-1) + dpB[n-1] * A</p><p>dpB[n] = dpA[n-1] * B + dpB[n-1] * (B-1)</p><p>Answer will be dpA[k]. So you have <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup> + <i>k</i>)</span> solution.</p><p>Also this problem can be solved in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/30663b28627443a73b3aed1e96e06b64506cfc8e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a></p><p><strong>C div1. E div2.</strong> The second player have easy strategy to hold some chip in position <span class=\"tex-span\">(<i>X</i>, <i>Y</i>)</span> in one of four half-planes — <span class=\"tex-span\"><i>x</i> ≤ <i>X</i> + 2</span>, <span class=\"tex-span\"><i>x</i> ≥ <i>X</i> - 2</span>, <span class=\"tex-span\"><i>y</i> ≤ <i>Y</i> + 2</span> и <span class=\"tex-span\"><i>y</i> ≥ <i>Y</i> - 2</span>. He can chose one of these half-planes by himself.</p><p>So, in case <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) > 4</span> the second player wins — he just holds chips in half-planes that have no common cells.</p><p>Cases for <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> expected to solve using some bruteforce. You can see that moving chips in way of distancing from each other is not profitable for the first player. Therefore you can bruteforce the game in square no more than <span class=\"tex-span\">5 × 5</span>. If your bruteforce so slow and doesn't fit into 2 sec, you can use precalculation. Also you can write some dp using masks.</p><p>Also you can check cases <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> by hand. But there you can easy make some mistakes.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>D div1.</strong> Let's define <span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>]</span> as the minimal prefix of hyperstring that have with prefix of <span class=\"tex-span\"><i>t</i></span> of length <span class=\"tex-span\"><i>len</i></span> largest common sequence of length <span class=\"tex-span\"><i>len</i></span>.</p><p>Then you have see reccurences:</p><p><span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>] = <i>min</i>(<i>dp</i>[<i>pre</i> - 1][<i>len</i>], </span> leftmost position of letter <span class=\"tex-span\"><i>s</i>[<i>pre</i>]</span> in <span class=\"tex-span\"><i>t</i></span> that right than <span class=\"tex-span\"><i>dp</i>[<i>pre</i> - 1][<i>len</i> - 1])</span>.</p><p>For finding value of the second part inside min-function of formula above in <span class=\"tex-span\"><i>O</i>(1)</span>, you should calculate some additional dp's: </p><p>dp1 — for every basic string, positions inside of them and letter you should calculate leftmost position of current letter that right than current position;</p><p>dp2 — for every element of array of basic strings (it is hyperstring) and letter you should calculate leftmost basic string that have current letter and this string is rinht than current basic string.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ab8527f1ac10b4b4d1feb948447ae95a2a57c78f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a>.</p><p><strong>E div1.</strong> At the first let's try to solve another problem: we have <span class=\"tex-span\"><i>k</i></span> chosed vertices in the tree and we want to find sum of subtree that "spanned" dy them in time <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (with any preprocessing time).</p><p>Let's sort all <span class=\"tex-span\"><i>k</i></span> vertices in order of dfs traversal — <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub></span>, ... , <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>k</i></sub></span>. Consider pathes v1-v2, v2-v3, ... , v(k-1)-vk and vk-v1. You can see that they cover only our requred subtree and every edge is covered exactly two times. So you can just find sum of lengths of these pathes (you can do it in required <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time using LCA algo) and divide obtained value by 2.</p><p>For solving initial problem you should support set of active vertices in ordered state (for example, you can use std::set) and sum of all pathes between all neighbour vertices. Now you can process insert/remove queries in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, and recalculate sum of pathes by finding no more than 3 new pathes also in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d61c652f63078ae0d26fbc9a95899f0f930104b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</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/176\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2</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/181\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2 (Unofficial Div. 2 Edition)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4386\").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: \"4372\",\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=croc-2012-round-2\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-2</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012</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-4386\"><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'>+43</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4386\"><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=\"Apr/20/2012 19:48\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4372#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/4372#comments\">\n 12\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=\"4396\">\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 (10)</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=\"88649\" 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/cholerikasi\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/44515/avatar/782a6a535da57281.jpg'/> </a>\n <div><a href=\"/profile/cholerikasi\" title=\"Specialist cholerikasi\" class=\"rated-user user-cyan\">cholerikasi</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 02:32\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88649\" href=\"?#comment-88649\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"88649\" 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=\"88649\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"44515\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88649\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For problem D (div 2) the formula is slightly incorrect. Correction:</p> <pre><code>dpA[n] = dpA[n-1]*(A-1) + dpB[n-1]*A\ndpB[n] = dpA[n-1]*B + dpB[n-1](B-1)\n</code></pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88649 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88649 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88649\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88932\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PrakharJain\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/27035/avatar/5784d107df6e4a90.jpg'/> </a>\n <div><a href=\"/profile/PrakharJain\" title=\"Candidate Master PrakharJain\" class=\"rated-user user-violet\">PrakharJain</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 00:40\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88932\" href=\"?#comment-88932\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88932\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"27035\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88932\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, you're right.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88932 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88932 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88932\">\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=\"88937\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Ripatti\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 01:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88937\" href=\"?#comment-88937\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88937\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"472\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88937\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you, fixed</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88937 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88937 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88937\">\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=\"88662\" 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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 11:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88662\" href=\"?#comment-88662\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88662\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88662\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In div2 E. Why does the second win when the input is "5 5 1 1 5 4"</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88662 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88662 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88662\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88686\" commentParentId=\"88662\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 15:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88686\" href=\"?#comment-88686\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88662\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88686\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88686\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Brute force proves it</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88686 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88686 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88686\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88688\" commentParentId=\"88686\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 16:01\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88688\" href=\"?#comment-88688\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88686\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88688\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88688\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Did you write the program using brute force and find the regularity before you submit the problem?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88688 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88688 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88688\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88735\" commentParentId=\"88688\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 18:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88735\" href=\"?#comment-88735\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88688\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88735\" 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=\"88735\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88735\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes I am. But I've got Wrong answer on test 9 and then write brute force.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88735 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88735 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88735\">\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=\"249677\" 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/yash_15\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/234147/avatar/2541b99b44dd628f.jpg'/> </a>\n <div><a href=\"/profile/yash_15\" title=\"Expert yash_15\" class=\"rated-user user-blue\">yash_15</a></div>\n </div>\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/06/2015 21:39\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249677\" href=\"?#comment-249677\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249677\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"234147\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249677\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For div 1 B, I want to know that what are values A and B in the recurrence relations? Also I would like to find some AC submissions to this problem.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249677 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249677 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249677\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"313733\" 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/haleyk100198\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a>\n <div><a href=\"/profile/haleyk100198\" title=\"Candidate Master haleyk100198\" class=\"rated-user user-violet\">haleyk100198</a></div>\n </div>\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/07/2016 16:54\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-313733\" href=\"?#comment-313733\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"313733\" 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=\"313733\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"416324\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-313733\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Div1E I have an alternative solution which focuses on binary searching the LCA of a point and a set of points as I didn't noticed that I can double count all necessary path by sorting dfs visiting time.</p><p>Code: <a href=\"//codeforces.com/contest/176/submission/20437271\">http://codeforces.com/contest/176/submission/20437271</a></p><p>(Now reviewing the code, the part of getLCA and sparse table is not required for finding LCA between a point and a set of points)</p><p>The current length of all necessary path is always updated.</p><p>Pre-processing:</p> <ol> <li><p>dfs for finding the visiting time and ending time of each vertex. O(N)</p></li> <li><p>Pre-calculate the binary exponential distance from each vertex to the 2^N parent. O(NlogN)</p></li> </ol><p>The current length of all necessary path is always kept</p><p>Keep a segment tree to check if there are any restored village in a sub-tree in O(logN) time, we will need it for the binary searches for the queries.</p><p>How to handle queries:</p><p>'+': Find two poitns: 1. the LCA of the village being restored with any other already restored villages, 2. the LCA of the new set of points. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>'-': Find two points: 1. the LCA of the remaining set, 2. the LCA of the village being destroyed with any other villages that are still available. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>Remember to handle cases where the restored villages set size if smaller than 2.</p><p>'?': Just return the length value, this can be done in O(1) time.</p><p>Total time complexity: O(NlogN + qlogN * logN), which is slightly worse than the intended solution but it still fits in the TL very easily.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-313733 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-313733 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-313733\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"713689\" 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/gabaswillwinIOI2022\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/gabaswillwinIOI2022\" title=\"Master gabaswillwinIOI2022\" class=\"rated-user user-orange\">gabaswillwinIOI2022</a></div>\n </div>\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/23/2020 14:32\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-713689\" href=\"?#comment-713689\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"713689\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1567470\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-713689\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>O(|w| + logk) solution for <a href=\"/contest/176/problem/B\" title=\"Croc Champ 2012 - Round 2\">176B - Word Cut</a> (Div 1 B) <a href=\"/contest/176/submission/96438522\" title=\"Submission 96438522 by gabaswillwinIOI2022\">96438522</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-713689 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-713689 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-713689\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4396\" 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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Word Cut"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Word Cut</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>Let's consider one interesting word game. In this game you should transform one word into another through special operations. </p><p>Let's say we have word <span class=\"tex-span\"><i>w</i></span>, let's split this word into two non-empty parts <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> so, that <span class=\"tex-span\"><i>w</i> = <i>xy</i></span>. A <span class=\"tex-font-style-it\">split</span> operation is transforming word <span class=\"tex-span\"><i>w</i> = <i>xy</i></span> into word <span class=\"tex-span\"><i>u</i> = <i>yx</i></span>. For example, a <span class=\"tex-font-style-it\">split</span> operation can transform word \"<span class=\"tex-font-style-tt\">wordcut</span>\" into word \"<span class=\"tex-font-style-tt\">cutword</span>\".</p><p>You are given two words <span class=\"tex-span\"><i>start</i></span> and <span class=\"tex-span\"><i>end</i></span>. Count in how many ways we can transform word <span class=\"tex-span\"><i>start</i></span> into word <span class=\"tex-span\"><i>end</i></span>, if we apply exactly <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-font-style-it\">split</span> operations consecutively to word <span class=\"tex-span\"><i>start</i></span>. </p><p>Two ways are considered different if the sequences of applied operations differ. Two operation sequences are different if exists such number <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>k</i></span>), that in the <span class=\"tex-span\"><i>i</i></span>-th operation of the first sequence the word splits into parts <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>, in the <span class=\"tex-span\"><i>i</i></span>-th operation of the second sequence the word splits into parts <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>, and additionally <span class=\"tex-span\"><i>x</i> ≠ <i>a</i></span> holds.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a non-empty word <span class=\"tex-span\"><i>start</i></span>, the second line contains a non-empty word <span class=\"tex-span\"><i>end</i></span>. The words consist of lowercase Latin letters. The number of letters in word <span class=\"tex-span\"><i>start</i></span> equals the number of letters in word <span class=\"tex-span\"><i>end</i></span> and is at least <span class=\"tex-span\">2</span> and doesn't exceed <span class=\"tex-span\">1000</span> letters.</p><p>The third 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 required number of operations.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the answer to the problem. As this number can be rather large, print it 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>ab<br/>ab<br/>2<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>ababab<br/>ababab<br/>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>ab<br/>ba<br/>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>The sought way in the first sample is:</p><p><span class=\"tex-font-style-tt\">ab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">a|b</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ba</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">b|a</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ab</span></p><p>In the second sample the two sought ways are:</p><ul><li> <span class=\"tex-font-style-tt\">ababab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">abab|ab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ababab</span> </li><li> <span class=\"tex-font-style-tt\">ababab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ab|abab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ababab</span></li></ul></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=\"dc5c82d1c9e6f6ff76d93e2fce964dc8\"/>\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=\"19756bd4dfb417b7c391f4abee7fa342560c6bd4\"/>\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 (!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_ff247ff509c6ce71a6956331b022d412b317894a\">\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. Word Cut</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>Let's consider one interesting word game. In this game you should transform one word into another through special operations. </p><p>Let's say we have word <span class=\"tex-span\"><i>w</i></span>, let's split this word into two non-empty parts <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> so, that <span class=\"tex-span\"><i>w</i> = <i>xy</i></span>. A <span class=\"tex-font-style-it\">split</span> operation is transforming word <span class=\"tex-span\"><i>w</i> = <i>xy</i></span> into word <span class=\"tex-span\"><i>u</i> = <i>yx</i></span>. For example, a <span class=\"tex-font-style-it\">split</span> operation can transform word "<span class=\"tex-font-style-tt\">wordcut</span>" into word "<span class=\"tex-font-style-tt\">cutword</span>".</p><p>You are given two words <span class=\"tex-span\"><i>start</i></span> and <span class=\"tex-span\"><i>end</i></span>. Count in how many ways we can transform word <span class=\"tex-span\"><i>start</i></span> into word <span class=\"tex-span\"><i>end</i></span>, if we apply exactly <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-font-style-it\">split</span> operations consecutively to word <span class=\"tex-span\"><i>start</i></span>. </p><p>Two ways are considered different if the sequences of applied operations differ. Two operation sequences are different if exists such number <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>k</i></span>), that in the <span class=\"tex-span\"><i>i</i></span>-th operation of the first sequence the word splits into parts <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>, in the <span class=\"tex-span\"><i>i</i></span>-th operation of the second sequence the word splits into parts <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>, and additionally <span class=\"tex-span\"><i>x</i> ≠ <i>a</i></span> holds.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a non-empty word <span class=\"tex-span\"><i>start</i></span>, the second line contains a non-empty word <span class=\"tex-span\"><i>end</i></span>. The words consist of lowercase Latin letters. The number of letters in word <span class=\"tex-span\"><i>start</i></span> equals the number of letters in word <span class=\"tex-span\"><i>end</i></span> and is at least <span class=\"tex-span\">2</span> and doesn't exceed <span class=\"tex-span\">1000</span> letters.</p><p>The third 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 required number of operations.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the answer to the problem. As this number can be rather large, print it 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>ab<br />ab<br />2<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>ababab<br />ababab<br />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>ab<br />ba<br />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>The sought way in the first sample is:</p><p><span class=\"tex-font-style-tt\">ab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">a|b</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ba</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">b|a</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ab</span></p><p>In the second sample the two sought ways are:</p><ul><li> <span class=\"tex-font-style-tt\">ababab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">abab|ab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ababab</span> </li><li> <span class=\"tex-font-style-tt\">ababab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ab|abab</span> <span class=\"tex-span\"> → </span> <span class=\"tex-font-style-tt\">ababab</span></li></ul></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 = 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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='15679b166c86ee80065b195f1dc12b4b'/>\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)\" 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/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=\"4386\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4372\"> <p>Croc Champ 2012 — Round 2 — Editorial</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=\"Apr/20/2012 19:48\">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>A div2.</strong> Required row is row that have only one star inside. Requred column is comumn that also have only one star inside. So, you can iterate over all rows/columns, calculate number of stars inside them and find the answer.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B div2.</strong> Naive solution <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> (where you check all triplets) doesn't fin into time limits.</p><p>You can see that for every two points from triplet (for example, for A and C) you can find place of the third point. So you can find number of requred triplets just inerate over all pairs of points and check middle point between points in every pair.</p><p>How to fast check position? You can add 1000 for all coordinates (you can see that this operation doesn't change the answer) and mark them in the 2-dimensional boolean array 2001х2001. So you can check every position for point in <span class=\"tex-span\"><i>O</i>(1)</span> time.</p><p>Obtained solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a></p><p><strong>A div1. C div2.</strong> In this problem some greedy solution expected.</p><p>Let fix 2 planets: in planet i we will buy items, in planet j we will sell the ones. <em>Profit of item</em> of type k will be b_jk-a_ik. Every item has size 1, so you should greedy take items in order of decreasing of profits of items while you have place in the hold.</p><p>Scheme of full solution: you should iterate over all pairs of planet, for every pair greedy take items and find total profit. At the end you should find maximal total profit over all pairs and output it.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>B div1. D div2.</strong> You can see that split oparetion is just cyclically shift of string. You can go from any cyclically shift to any other one except the current one.</p><p>Let's call some cyclically shift <em>good</em> iff it equal to the final string. All others cyclically shifts we will call <em>bad</em>. You can check all shifts in <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup>)</span> time. Let's you have A good shifts and B bad ones.</p><p>Let's define dpA[n] as number of ways to get some good shift using n splits and за dpB[n] as number of ways to get some bad shift using n splits.</p><p>dpA[0]=1, dpB[0]=0 or dpA[0]=0, dpB[0]=1 according to the first shift is good or not. All other values of dp you can get using following reccurences:</p><p>dpA[n] = dpA[n-1] * (A-1) + dpB[n-1] * A</p><p>dpB[n] = dpA[n-1] * B + dpB[n-1] * (B-1)</p><p>Answer will be dpA[k]. So you have <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup> + <i>k</i>)</span> solution.</p><p>Also this problem can be solved in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/30663b28627443a73b3aed1e96e06b64506cfc8e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a></p><p><strong>C div1. E div2.</strong> The second player have easy strategy to hold some chip in position <span class=\"tex-span\">(<i>X</i>, <i>Y</i>)</span> in one of four half-planes — <span class=\"tex-span\"><i>x</i> ≤ <i>X</i> + 2</span>, <span class=\"tex-span\"><i>x</i> ≥ <i>X</i> - 2</span>, <span class=\"tex-span\"><i>y</i> ≤ <i>Y</i> + 2</span> и <span class=\"tex-span\"><i>y</i> ≥ <i>Y</i> - 2</span>. He can chose one of these half-planes by himself.</p><p>So, in case <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) > 4</span> the second player wins — he just holds chips in half-planes that have no common cells.</p><p>Cases for <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> expected to solve using some bruteforce. You can see that moving chips in way of distancing from each other is not profitable for the first player. Therefore you can bruteforce the game in square no more than <span class=\"tex-span\">5 × 5</span>. If your bruteforce so slow and doesn't fit into 2 sec, you can use precalculation. Also you can write some dp using masks.</p><p>Also you can check cases <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> by hand. But there you can easy make some mistakes.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>D div1.</strong> Let's define <span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>]</span> as the minimal prefix of hyperstring that have with prefix of <span class=\"tex-span\"><i>t</i></span> of length <span class=\"tex-span\"><i>len</i></span> largest common sequence of length <span class=\"tex-span\"><i>len</i></span>.</p><p>Then you have see reccurences:</p><p><span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>] = <i>min</i>(<i>dp</i>[<i>pre</i> - 1][<i>len</i>], </span> leftmost position of letter <span class=\"tex-span\"><i>s</i>[<i>pre</i>]</span> in <span class=\"tex-span\"><i>t</i></span> that right than <span class=\"tex-span\"><i>dp</i>[<i>pre</i> - 1][<i>len</i> - 1])</span>.</p><p>For finding value of the second part inside min-function of formula above in <span class=\"tex-span\"><i>O</i>(1)</span>, you should calculate some additional dp's: </p><p>dp1 — for every basic string, positions inside of them and letter you should calculate leftmost position of current letter that right than current position;</p><p>dp2 — for every element of array of basic strings (it is hyperstring) and letter you should calculate leftmost basic string that have current letter and this string is rinht than current basic string.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ab8527f1ac10b4b4d1feb948447ae95a2a57c78f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a>.</p><p><strong>E div1.</strong> At the first let's try to solve another problem: we have <span class=\"tex-span\"><i>k</i></span> chosed vertices in the tree and we want to find sum of subtree that "spanned" dy them in time <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (with any preprocessing time).</p><p>Let's sort all <span class=\"tex-span\"><i>k</i></span> vertices in order of dfs traversal — <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub></span>, ... , <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>k</i></sub></span>. Consider pathes v1-v2, v2-v3, ... , v(k-1)-vk and vk-v1. You can see that they cover only our requred subtree and every edge is covered exactly two times. So you can just find sum of lengths of these pathes (you can do it in required <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time using LCA algo) and divide obtained value by 2.</p><p>For solving initial problem you should support set of active vertices in ordered state (for example, you can use std::set) and sum of all pathes between all neighbour vertices. Now you can process insert/remove queries in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, and recalculate sum of pathes by finding no more than 3 new pathes also in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d61c652f63078ae0d26fbc9a95899f0f930104b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</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/176\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2</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/181\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2 (Unofficial Div. 2 Edition)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4386\").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: \"4372\",\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=croc-2012-round-2\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-2</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012</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-4386\"><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'>+43</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4386\"><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=\"Apr/20/2012 19:48\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4372#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/4372#comments\">\n 12\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=\"4396\">\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 (10)</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=\"88649\" 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/cholerikasi\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/44515/avatar/782a6a535da57281.jpg'/> </a>\n <div><a href=\"/profile/cholerikasi\" title=\"Specialist cholerikasi\" class=\"rated-user user-cyan\">cholerikasi</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 02:32\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88649\" href=\"?#comment-88649\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"88649\" 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=\"88649\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"44515\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88649\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For problem D (div 2) the formula is slightly incorrect. Correction:</p> <pre><code>dpA[n] = dpA[n-1]*(A-1) + dpB[n-1]*A\ndpB[n] = dpA[n-1]*B + dpB[n-1](B-1)\n</code></pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88649 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88649 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88649\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88932\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PrakharJain\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/27035/avatar/5784d107df6e4a90.jpg'/> </a>\n <div><a href=\"/profile/PrakharJain\" title=\"Candidate Master PrakharJain\" class=\"rated-user user-violet\">PrakharJain</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 00:40\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88932\" href=\"?#comment-88932\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88932\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"27035\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88932\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, you're right.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88932 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88932 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88932\">\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=\"88937\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Ripatti\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 01:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88937\" href=\"?#comment-88937\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88937\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"472\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88937\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you, fixed</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88937 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88937 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88937\">\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=\"88662\" 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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 11:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88662\" href=\"?#comment-88662\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88662\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88662\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In div2 E. Why does the second win when the input is "5 5 1 1 5 4"</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88662 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88662 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88662\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88686\" commentParentId=\"88662\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 15:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88686\" href=\"?#comment-88686\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88662\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88686\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88686\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Brute force proves it</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88686 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88686 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88686\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88688\" commentParentId=\"88686\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 16:01\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88688\" href=\"?#comment-88688\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88686\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88688\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88688\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Did you write the program using brute force and find the regularity before you submit the problem?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88688 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88688 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88688\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88735\" commentParentId=\"88688\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 18:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88735\" href=\"?#comment-88735\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88688\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88735\" 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=\"88735\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88735\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes I am. But I've got Wrong answer on test 9 and then write brute force.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88735 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88735 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88735\">\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=\"249677\" 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/yash_15\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/234147/avatar/2541b99b44dd628f.jpg'/> </a>\n <div><a href=\"/profile/yash_15\" title=\"Expert yash_15\" class=\"rated-user user-blue\">yash_15</a></div>\n </div>\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/06/2015 21:39\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249677\" href=\"?#comment-249677\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249677\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"234147\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249677\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For div 1 B, I want to know that what are values A and B in the recurrence relations? Also I would like to find some AC submissions to this problem.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249677 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249677 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249677\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"313733\" 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/haleyk100198\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a>\n <div><a href=\"/profile/haleyk100198\" title=\"Candidate Master haleyk100198\" class=\"rated-user user-violet\">haleyk100198</a></div>\n </div>\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/07/2016 16:54\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-313733\" href=\"?#comment-313733\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"313733\" 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=\"313733\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"416324\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-313733\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Div1E I have an alternative solution which focuses on binary searching the LCA of a point and a set of points as I didn't noticed that I can double count all necessary path by sorting dfs visiting time.</p><p>Code: <a href=\"//codeforces.com/contest/176/submission/20437271\">http://codeforces.com/contest/176/submission/20437271</a></p><p>(Now reviewing the code, the part of getLCA and sparse table is not required for finding LCA between a point and a set of points)</p><p>The current length of all necessary path is always updated.</p><p>Pre-processing:</p> <ol> <li><p>dfs for finding the visiting time and ending time of each vertex. O(N)</p></li> <li><p>Pre-calculate the binary exponential distance from each vertex to the 2^N parent. O(NlogN)</p></li> </ol><p>The current length of all necessary path is always kept</p><p>Keep a segment tree to check if there are any restored village in a sub-tree in O(logN) time, we will need it for the binary searches for the queries.</p><p>How to handle queries:</p><p>'+': Find two poitns: 1. the LCA of the village being restored with any other already restored villages, 2. the LCA of the new set of points. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>'-': Find two points: 1. the LCA of the remaining set, 2. the LCA of the village being destroyed with any other villages that are still available. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>Remember to handle cases where the restored villages set size if smaller than 2.</p><p>'?': Just return the length value, this can be done in O(1) time.</p><p>Total time complexity: O(NlogN + qlogN * logN), which is slightly worse than the intended solution but it still fits in the TL very easily.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-313733 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-313733 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-313733\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"713689\" 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/gabaswillwinIOI2022\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/gabaswillwinIOI2022\" title=\"Master gabaswillwinIOI2022\" class=\"rated-user user-orange\">gabaswillwinIOI2022</a></div>\n </div>\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/23/2020 14:32\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-713689\" href=\"?#comment-713689\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"713689\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1567470\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-713689\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>O(|w| + logk) solution for <a href=\"/contest/176/problem/B\" title=\"Croc Champ 2012 - Round 2\">176B - Word Cut</a> (Div 1 B) <a href=\"/contest/176/submission/96438522\" title=\"Submission 96438522 by gabaswillwinIOI2022\">96438522</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-713689 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-713689 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-713689\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4396\" 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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Playing with Superglue"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Playing with Superglue</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>Two players play a game. The game is played on a rectangular board with <span class=\"tex-span\"><i>n</i> × <i>m</i></span> squares. At the beginning of the game two different squares of the board have two chips. The first player's goal is to shift the chips to the same square. The second player aims to stop the first one with a <span class=\"tex-font-style-it\">tube of superglue</span>.</p><p>We'll describe the rules of the game in more detail.</p><p>The players move in turns. The first player begins.</p><p>With every move the first player chooses one of his unglued chips, and shifts it one square to the left, to the right, up or down. It is not allowed to move a chip beyond the board edge. At the beginning of a turn some squares of the board may be covered with a glue. The first player can move the chip to such square, in this case the chip gets tightly glued and cannot move any longer.</p><p>At each move the second player selects one of the free squares (which do not contain a chip or a glue) and covers it with superglue. The glue dries long and squares covered with it remain sticky up to the end of the game.</p><p>If, after some move of the first player both chips are in the same square, then the first player wins. If the first player cannot make a move (both of his chips are glued), then the second player wins. Note that the situation where the second player cannot make a move is impossible — he can always spread the glue on the square from which the first player has just moved the chip.</p><p>We will further clarify the case where both chips are glued and are in the same square. In this case the first player wins as the game ends as soon as both chips are in the same square, and the condition of the loss (the inability to move) does not arise.</p><p>You know the board sizes and the positions of the two chips on it. At the beginning of the game all board squares are glue-free. Find out who wins if the players play optimally.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains six integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">2</sub></span> — the board sizes and the coordinates of the first and second chips, correspondingly (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 100</span>; <span class=\"tex-span\">2 ≤ <i>n</i> × <i>m</i></span>; <span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> ≤ <i>n</i></span>; <span class=\"tex-span\">1 ≤ <i>y</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">2</sub> ≤ <i>m</i></span>). The numbers in the line are separated by single spaces.</p><p>It is guaranteed that the chips are located in different squares.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If the first player wins, 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>1 6 1 2 1 6<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 5 4 3 2 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>10 10 1 1 10 10<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Second</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=\"e4588006969ab72c8e20436375d86bb7\"/>\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 - 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=\"19756bd4dfb417b7c391f4abee7fa342560c6bd4\"/>\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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|| 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_d3df570daab3d50deaf4c1e203df34fa0e4a6b42\">\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. Playing with Superglue</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>Two players play a game. The game is played on a rectangular board with <span class=\"tex-span\"><i>n</i> × <i>m</i></span> squares. At the beginning of the game two different squares of the board have two chips. The first player's goal is to shift the chips to the same square. The second player aims to stop the first one with a <span class=\"tex-font-style-it\">tube of superglue</span>.</p><p>We'll describe the rules of the game in more detail.</p><p>The players move in turns. The first player begins.</p><p>With every move the first player chooses one of his unglued chips, and shifts it one square to the left, to the right, up or down. It is not allowed to move a chip beyond the board edge. At the beginning of a turn some squares of the board may be covered with a glue. The first player can move the chip to such square, in this case the chip gets tightly glued and cannot move any longer.</p><p>At each move the second player selects one of the free squares (which do not contain a chip or a glue) and covers it with superglue. The glue dries long and squares covered with it remain sticky up to the end of the game.</p><p>If, after some move of the first player both chips are in the same square, then the first player wins. If the first player cannot make a move (both of his chips are glued), then the second player wins. Note that the situation where the second player cannot make a move is impossible — he can always spread the glue on the square from which the first player has just moved the chip.</p><p>We will further clarify the case where both chips are glued and are in the same square. In this case the first player wins as the game ends as soon as both chips are in the same square, and the condition of the loss (the inability to move) does not arise.</p><p>You know the board sizes and the positions of the two chips on it. At the beginning of the game all board squares are glue-free. Find out who wins if the players play optimally.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains six integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">2</sub></span> — the board sizes and the coordinates of the first and second chips, correspondingly (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 100</span>; <span class=\"tex-span\">2 ≤ <i>n</i> × <i>m</i></span>; <span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> ≤ <i>n</i></span>; <span class=\"tex-span\">1 ≤ <i>y</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">2</sub> ≤ <i>m</i></span>). The numbers in the line are separated by single spaces.</p><p>It is guaranteed that the chips are located in different squares.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If the first player wins, 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>1 6 1 2 1 6<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 5 4 3 2 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>10 10 1 1 10 10<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Second</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 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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=''>13:54:57</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='15679b166c86ee80065b195f1dc12b4b'/>\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=\"4386\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4372\"> <p>Croc Champ 2012 — Round 2 — Editorial</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=\"Apr/20/2012 19:48\">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>A div2.</strong> Required row is row that have only one star inside. Requred column is comumn that also have only one star inside. So, you can iterate over all rows/columns, calculate number of stars inside them and find the answer.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B div2.</strong> Naive solution <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> (where you check all triplets) doesn't fin into time limits.</p><p>You can see that for every two points from triplet (for example, for A and C) you can find place of the third point. So you can find number of requred triplets just inerate over all pairs of points and check middle point between points in every pair.</p><p>How to fast check position? You can add 1000 for all coordinates (you can see that this operation doesn't change the answer) and mark them in the 2-dimensional boolean array 2001х2001. So you can check every position for point in <span class=\"tex-span\"><i>O</i>(1)</span> time.</p><p>Obtained solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a></p><p><strong>A div1. C div2.</strong> In this problem some greedy solution expected.</p><p>Let fix 2 planets: in planet i we will buy items, in planet j we will sell the ones. <em>Profit of item</em> of type k will be b_jk-a_ik. Every item has size 1, so you should greedy take items in order of decreasing of profits of items while you have place in the hold.</p><p>Scheme of full solution: you should iterate over all pairs of planet, for every pair greedy take items and find total profit. At the end you should find maximal total profit over all pairs and output it.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>B div1. D div2.</strong> You can see that split oparetion is just cyclically shift of string. You can go from any cyclically shift to any other one except the current one.</p><p>Let's call some cyclically shift <em>good</em> iff it equal to the final string. All others cyclically shifts we will call <em>bad</em>. You can check all shifts in <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup>)</span> time. Let's you have A good shifts and B bad ones.</p><p>Let's define dpA[n] as number of ways to get some good shift using n splits and за dpB[n] as number of ways to get some bad shift using n splits.</p><p>dpA[0]=1, dpB[0]=0 or dpA[0]=0, dpB[0]=1 according to the first shift is good or not. All other values of dp you can get using following reccurences:</p><p>dpA[n] = dpA[n-1] * (A-1) + dpB[n-1] * A</p><p>dpB[n] = dpA[n-1] * B + dpB[n-1] * (B-1)</p><p>Answer will be dpA[k]. So you have <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup> + <i>k</i>)</span> solution.</p><p>Also this problem can be solved in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/30663b28627443a73b3aed1e96e06b64506cfc8e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a></p><p><strong>C div1. E div2.</strong> The second player have easy strategy to hold some chip in position <span class=\"tex-span\">(<i>X</i>, <i>Y</i>)</span> in one of four half-planes — <span class=\"tex-span\"><i>x</i> ≤ <i>X</i> + 2</span>, <span class=\"tex-span\"><i>x</i> ≥ <i>X</i> - 2</span>, <span class=\"tex-span\"><i>y</i> ≤ <i>Y</i> + 2</span> и <span class=\"tex-span\"><i>y</i> ≥ <i>Y</i> - 2</span>. He can chose one of these half-planes by himself.</p><p>So, in case <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) > 4</span> the second player wins — he just holds chips in half-planes that have no common cells.</p><p>Cases for <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> expected to solve using some bruteforce. You can see that moving chips in way of distancing from each other is not profitable for the first player. Therefore you can bruteforce the game in square no more than <span class=\"tex-span\">5 × 5</span>. If your bruteforce so slow and doesn't fit into 2 sec, you can use precalculation. Also you can write some dp using masks.</p><p>Also you can check cases <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> by hand. But there you can easy make some mistakes.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>D div1.</strong> Let's define <span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>]</span> as the minimal prefix of hyperstring that have with prefix of <span class=\"tex-span\"><i>t</i></span> of length <span class=\"tex-span\"><i>len</i></span> largest common sequence of length <span class=\"tex-span\"><i>len</i></span>.</p><p>Then you have see reccurences:</p><p><span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>] = <i>min</i>(<i>dp</i>[<i>pre</i> - 1][<i>len</i>], </span> leftmost position of letter <span class=\"tex-span\"><i>s</i>[<i>pre</i>]</span> in <span class=\"tex-span\"><i>t</i></span> that right than <span class=\"tex-span\"><i>dp</i>[<i>pre</i> - 1][<i>len</i> - 1])</span>.</p><p>For finding value of the second part inside min-function of formula above in <span class=\"tex-span\"><i>O</i>(1)</span>, you should calculate some additional dp's: </p><p>dp1 — for every basic string, positions inside of them and letter you should calculate leftmost position of current letter that right than current position;</p><p>dp2 — for every element of array of basic strings (it is hyperstring) and letter you should calculate leftmost basic string that have current letter and this string is rinht than current basic string.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ab8527f1ac10b4b4d1feb948447ae95a2a57c78f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a>.</p><p><strong>E div1.</strong> At the first let's try to solve another problem: we have <span class=\"tex-span\"><i>k</i></span> chosed vertices in the tree and we want to find sum of subtree that "spanned" dy them in time <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (with any preprocessing time).</p><p>Let's sort all <span class=\"tex-span\"><i>k</i></span> vertices in order of dfs traversal — <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub></span>, ... , <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>k</i></sub></span>. Consider pathes v1-v2, v2-v3, ... , v(k-1)-vk and vk-v1. You can see that they cover only our requred subtree and every edge is covered exactly two times. So you can just find sum of lengths of these pathes (you can do it in required <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time using LCA algo) and divide obtained value by 2.</p><p>For solving initial problem you should support set of active vertices in ordered state (for example, you can use std::set) and sum of all pathes between all neighbour vertices. Now you can process insert/remove queries in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, and recalculate sum of pathes by finding no more than 3 new pathes also in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d61c652f63078ae0d26fbc9a95899f0f930104b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</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/176\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2</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/181\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2 (Unofficial Div. 2 Edition)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4386\").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: \"4372\",\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=croc-2012-round-2\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-2</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012</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-4386\"><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'>+43</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4386\"><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=\"Apr/20/2012 19:48\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4372#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/4372#comments\">\n 12\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=\"4396\">\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 (10)</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=\"88649\" 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/cholerikasi\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/44515/avatar/782a6a535da57281.jpg'/> </a>\n <div><a href=\"/profile/cholerikasi\" title=\"Specialist cholerikasi\" class=\"rated-user user-cyan\">cholerikasi</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 02:32\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88649\" href=\"?#comment-88649\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"88649\" 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=\"88649\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"44515\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88649\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For problem D (div 2) the formula is slightly incorrect. Correction:</p> <pre><code>dpA[n] = dpA[n-1]*(A-1) + dpB[n-1]*A\ndpB[n] = dpA[n-1]*B + dpB[n-1](B-1)\n</code></pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88649 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88649 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88649\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88932\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PrakharJain\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/27035/avatar/5784d107df6e4a90.jpg'/> </a>\n <div><a href=\"/profile/PrakharJain\" title=\"Candidate Master PrakharJain\" class=\"rated-user user-violet\">PrakharJain</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 00:40\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88932\" href=\"?#comment-88932\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88932\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"27035\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88932\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, you're right.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88932 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88932 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88932\">\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=\"88937\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Ripatti\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 01:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88937\" href=\"?#comment-88937\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88937\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"472\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88937\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you, fixed</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88937 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88937 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88937\">\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=\"88662\" 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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 11:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88662\" href=\"?#comment-88662\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88662\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88662\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In div2 E. Why does the second win when the input is "5 5 1 1 5 4"</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88662 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88662 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88662\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88686\" commentParentId=\"88662\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 15:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88686\" href=\"?#comment-88686\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88662\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88686\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88686\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Brute force proves it</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88686 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88686 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88686\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88688\" commentParentId=\"88686\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 16:01\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88688\" href=\"?#comment-88688\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88686\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88688\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88688\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Did you write the program using brute force and find the regularity before you submit the problem?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88688 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88688 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88688\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88735\" commentParentId=\"88688\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 18:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88735\" href=\"?#comment-88735\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88688\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88735\" 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=\"88735\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88735\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes I am. But I've got Wrong answer on test 9 and then write brute force.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88735 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88735 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88735\">\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=\"249677\" 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/yash_15\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/234147/avatar/2541b99b44dd628f.jpg'/> </a>\n <div><a href=\"/profile/yash_15\" title=\"Expert yash_15\" class=\"rated-user user-blue\">yash_15</a></div>\n </div>\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/06/2015 21:39\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249677\" href=\"?#comment-249677\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249677\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"234147\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249677\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For div 1 B, I want to know that what are values A and B in the recurrence relations? Also I would like to find some AC submissions to this problem.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249677 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249677 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249677\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"313733\" 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/haleyk100198\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a>\n <div><a href=\"/profile/haleyk100198\" title=\"Candidate Master haleyk100198\" class=\"rated-user user-violet\">haleyk100198</a></div>\n </div>\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/07/2016 16:54\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-313733\" href=\"?#comment-313733\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"313733\" 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=\"313733\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"416324\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-313733\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Div1E I have an alternative solution which focuses on binary searching the LCA of a point and a set of points as I didn't noticed that I can double count all necessary path by sorting dfs visiting time.</p><p>Code: <a href=\"//codeforces.com/contest/176/submission/20437271\">http://codeforces.com/contest/176/submission/20437271</a></p><p>(Now reviewing the code, the part of getLCA and sparse table is not required for finding LCA between a point and a set of points)</p><p>The current length of all necessary path is always updated.</p><p>Pre-processing:</p> <ol> <li><p>dfs for finding the visiting time and ending time of each vertex. O(N)</p></li> <li><p>Pre-calculate the binary exponential distance from each vertex to the 2^N parent. O(NlogN)</p></li> </ol><p>The current length of all necessary path is always kept</p><p>Keep a segment tree to check if there are any restored village in a sub-tree in O(logN) time, we will need it for the binary searches for the queries.</p><p>How to handle queries:</p><p>'+': Find two poitns: 1. the LCA of the village being restored with any other already restored villages, 2. the LCA of the new set of points. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>'-': Find two points: 1. the LCA of the remaining set, 2. the LCA of the village being destroyed with any other villages that are still available. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>Remember to handle cases where the restored villages set size if smaller than 2.</p><p>'?': Just return the length value, this can be done in O(1) time.</p><p>Total time complexity: O(NlogN + qlogN * logN), which is slightly worse than the intended solution but it still fits in the TL very easily.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-313733 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-313733 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-313733\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"713689\" 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/gabaswillwinIOI2022\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/gabaswillwinIOI2022\" title=\"Master gabaswillwinIOI2022\" class=\"rated-user user-orange\">gabaswillwinIOI2022</a></div>\n </div>\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/23/2020 14:32\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-713689\" href=\"?#comment-713689\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"713689\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1567470\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-713689\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>O(|w| + logk) solution for <a href=\"/contest/176/problem/B\" title=\"Croc Champ 2012 - Round 2\">176B - Word Cut</a> (Div 1 B) <a href=\"/contest/176/submission/96438522\" title=\"Submission 96438522 by gabaswillwinIOI2022\">96438522</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-713689 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-713689 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-713689\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4396\" 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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Hyper String"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Hyper 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>Paul Erdős's prediction came true. Finally an alien force landed on the Earth. In contrary to our expectation they didn't asked the humans to compute the value of a Ramsey number (maybe they had solved it themselves). They asked another question which seemed as hard as calculating Ramsey numbers. Aliens threatened that if humans don't solve this problem in less than 2 hours they will destroy the Earth. </p><p>Before telling the problem they introduced the concept of Hyper Strings. A Hyper String is made by concatenation of some base strings. Suppose you are given a list of base strings <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>n</i></sub></span>. Now the Hyper String made from indices list <span class=\"tex-span\"><i>i</i><sub class=\"lower-index\">1</sub>, <i>i</i><sub class=\"lower-index\">2</sub>, ..., <i>i</i><sub class=\"lower-index\"><i>m</i></sub></span> is concatenation of base strings <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\">1</sub></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\">2</sub></sub>, ..., <i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\"><i>m</i></sub></sub></span>. A Hyper String can be very large and doing operations on it is very costly for computers. </p><p>The aliens asked humans to compute the length of the longest common sub-sequence of a Hyper String <span class=\"tex-span\"><i>t</i></span> with a string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains the single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span>) — the number of base strings. </p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contains values of base strings. Each base string is made of lowercase Latin letters. A base string cannot be empty string and the sum of lengths of all <span class=\"tex-span\"><i>n</i></span> base strings doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>. </p><p>The next line contains the single integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span>) — the number of base strings in the given Hyper String <span class=\"tex-span\"><i>t</i></span>. </p><p>The next line contains <span class=\"tex-span\"><i>m</i></span> space-separated integer numbers <span class=\"tex-span\"><i>i</i><sub class=\"lower-index\">1</sub>, <i>i</i><sub class=\"lower-index\">2</sub>, ..., <i>i</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i><sub class=\"lower-index\"><i>j</i></sub> ≤ <i>n</i></span>) — the indices of base strings in the Hyper String <span class=\"tex-span\"><i>t</i></span>.</p><p>The last line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>. String <span class=\"tex-span\"><i>s</i></span> is made of lowercase Latin letters and its length is no more than <span class=\"tex-span\">2000</span> characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the length of longest common sub-sequence of Hyper String <span class=\"tex-span\"><i>t</i></span> and string <span class=\"tex-span\"><i>s</i></span>. If there is no common sub-sequence print 0.</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<br/>cba<br/>dgh<br/>2<br/>1 2<br/>aedfhr<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>2<br/>b<br/>a<br/>5<br/>1 2 1 2 1<br/>aaa<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>The <span class=\"tex-font-style-it\">length</span> of string <span class=\"tex-span\"><i>s</i></span> is the number of characters in it. If the length of string <span class=\"tex-span\"><i>s</i></span> is marked as <span class=\"tex-span\">|<i>s</i>|</span>, then string <span class=\"tex-span\"><i>s</i></span> can be represented as <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>y</i> = <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>y</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>y</i>|</sub></sub></span> (<span class=\"tex-span\">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>y</i>|</sub> ≤ |<i>s</i>|</span>) is a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i></span>. For example, \"<span class=\"tex-font-style-tt\">coders</span>\" is a subsequence of \"<span class=\"tex-font-style-tt\">codeforces</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=\"6e3115cef554167442a46865041100aa\"/>\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 - 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=\"19756bd4dfb417b7c391f4abee7fa342560c6bd4\"/>\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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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_ecf1d10e46b86d3ff27e74ecb80bf3dbb0377701\">\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. Hyper 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>Paul Erdős's prediction came true. Finally an alien force landed on the Earth. In contrary to our expectation they didn't asked the humans to compute the value of a Ramsey number (maybe they had solved it themselves). They asked another question which seemed as hard as calculating Ramsey numbers. Aliens threatened that if humans don't solve this problem in less than 2 hours they will destroy the Earth. </p><p>Before telling the problem they introduced the concept of Hyper Strings. A Hyper String is made by concatenation of some base strings. Suppose you are given a list of base strings <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>n</i></sub></span>. Now the Hyper String made from indices list <span class=\"tex-span\"><i>i</i><sub class=\"lower-index\">1</sub>, <i>i</i><sub class=\"lower-index\">2</sub>, ..., <i>i</i><sub class=\"lower-index\"><i>m</i></sub></span> is concatenation of base strings <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\">1</sub></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\">2</sub></sub>, ..., <i>b</i><sub class=\"lower-index\"><i>i</i><sub class=\"lower-index\"><i>m</i></sub></sub></span>. A Hyper String can be very large and doing operations on it is very costly for computers. </p><p>The aliens asked humans to compute the length of the longest common sub-sequence of a Hyper String <span class=\"tex-span\"><i>t</i></span> with a string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains the single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span>) — the number of base strings. </p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contains values of base strings. Each base string is made of lowercase Latin letters. A base string cannot be empty string and the sum of lengths of all <span class=\"tex-span\"><i>n</i></span> base strings doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">6</sup></span>. </p><p>The next line contains the single integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span>) — the number of base strings in the given Hyper String <span class=\"tex-span\"><i>t</i></span>. </p><p>The next line contains <span class=\"tex-span\"><i>m</i></span> space-separated integer numbers <span class=\"tex-span\"><i>i</i><sub class=\"lower-index\">1</sub>, <i>i</i><sub class=\"lower-index\">2</sub>, ..., <i>i</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i><sub class=\"lower-index\"><i>j</i></sub> ≤ <i>n</i></span>) — the indices of base strings in the Hyper String <span class=\"tex-span\"><i>t</i></span>.</p><p>The last line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>. String <span class=\"tex-span\"><i>s</i></span> is made of lowercase Latin letters and its length is no more than <span class=\"tex-span\">2000</span> characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the length of longest common sub-sequence of Hyper String <span class=\"tex-span\"><i>t</i></span> and string <span class=\"tex-span\"><i>s</i></span>. If there is no common sub-sequence print 0.</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<br />cba<br />dgh<br />2<br />1 2<br />aedfhr<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>2<br />b<br />a<br />5<br />1 2 1 2 1<br />aaa<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>The <span class=\"tex-font-style-it\">length</span> of string <span class=\"tex-span\"><i>s</i></span> is the number of characters in it. If the length of string <span class=\"tex-span\"><i>s</i></span> is marked as <span class=\"tex-span\">|<i>s</i>|</span>, then string <span class=\"tex-span\"><i>s</i></span> can be represented as <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>y</i> = <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>y</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>y</i>|</sub></sub></span> (<span class=\"tex-span\">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>y</i>|</sub> ≤ |<i>s</i>|</span>) is a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i></span>. For example, "<span class=\"tex-font-style-tt\">coders</span>" is a subsequence of "<span class=\"tex-font-style-tt\">codeforces</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: previousStatementText, b: statementText}, function (result) {\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='15679b166c86ee80065b195f1dc12b4b'/>\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)\" 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/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=\"4386\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4372\"> <p>Croc Champ 2012 — Round 2 — Editorial</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=\"Apr/20/2012 19:48\">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>A div2.</strong> Required row is row that have only one star inside. Requred column is comumn that also have only one star inside. So, you can iterate over all rows/columns, calculate number of stars inside them and find the answer.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B div2.</strong> Naive solution <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> (where you check all triplets) doesn't fin into time limits.</p><p>You can see that for every two points from triplet (for example, for A and C) you can find place of the third point. So you can find number of requred triplets just inerate over all pairs of points and check middle point between points in every pair.</p><p>How to fast check position? You can add 1000 for all coordinates (you can see that this operation doesn't change the answer) and mark them in the 2-dimensional boolean array 2001х2001. So you can check every position for point in <span class=\"tex-span\"><i>O</i>(1)</span> time.</p><p>Obtained solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a></p><p><strong>A div1. C div2.</strong> In this problem some greedy solution expected.</p><p>Let fix 2 planets: in planet i we will buy items, in planet j we will sell the ones. <em>Profit of item</em> of type k will be b_jk-a_ik. Every item has size 1, so you should greedy take items in order of decreasing of profits of items while you have place in the hold.</p><p>Scheme of full solution: you should iterate over all pairs of planet, for every pair greedy take items and find total profit. At the end you should find maximal total profit over all pairs and output it.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>B div1. D div2.</strong> You can see that split oparetion is just cyclically shift of string. You can go from any cyclically shift to any other one except the current one.</p><p>Let's call some cyclically shift <em>good</em> iff it equal to the final string. All others cyclically shifts we will call <em>bad</em>. You can check all shifts in <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup>)</span> time. Let's you have A good shifts and B bad ones.</p><p>Let's define dpA[n] as number of ways to get some good shift using n splits and за dpB[n] as number of ways to get some bad shift using n splits.</p><p>dpA[0]=1, dpB[0]=0 or dpA[0]=0, dpB[0]=1 according to the first shift is good or not. All other values of dp you can get using following reccurences:</p><p>dpA[n] = dpA[n-1] * (A-1) + dpB[n-1] * A</p><p>dpB[n] = dpA[n-1] * B + dpB[n-1] * (B-1)</p><p>Answer will be dpA[k]. So you have <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup> + <i>k</i>)</span> solution.</p><p>Also this problem can be solved in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/30663b28627443a73b3aed1e96e06b64506cfc8e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a></p><p><strong>C div1. E div2.</strong> The second player have easy strategy to hold some chip in position <span class=\"tex-span\">(<i>X</i>, <i>Y</i>)</span> in one of four half-planes — <span class=\"tex-span\"><i>x</i> ≤ <i>X</i> + 2</span>, <span class=\"tex-span\"><i>x</i> ≥ <i>X</i> - 2</span>, <span class=\"tex-span\"><i>y</i> ≤ <i>Y</i> + 2</span> и <span class=\"tex-span\"><i>y</i> ≥ <i>Y</i> - 2</span>. He can chose one of these half-planes by himself.</p><p>So, in case <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) > 4</span> the second player wins — he just holds chips in half-planes that have no common cells.</p><p>Cases for <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> expected to solve using some bruteforce. You can see that moving chips in way of distancing from each other is not profitable for the first player. Therefore you can bruteforce the game in square no more than <span class=\"tex-span\">5 × 5</span>. If your bruteforce so slow and doesn't fit into 2 sec, you can use precalculation. Also you can write some dp using masks.</p><p>Also you can check cases <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> by hand. But there you can easy make some mistakes.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>D div1.</strong> Let's define <span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>]</span> as the minimal prefix of hyperstring that have with prefix of <span class=\"tex-span\"><i>t</i></span> of length <span class=\"tex-span\"><i>len</i></span> largest common sequence of length <span class=\"tex-span\"><i>len</i></span>.</p><p>Then you have see reccurences:</p><p><span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>] = <i>min</i>(<i>dp</i>[<i>pre</i> - 1][<i>len</i>], </span> leftmost position of letter <span class=\"tex-span\"><i>s</i>[<i>pre</i>]</span> in <span class=\"tex-span\"><i>t</i></span> that right than <span class=\"tex-span\"><i>dp</i>[<i>pre</i> - 1][<i>len</i> - 1])</span>.</p><p>For finding value of the second part inside min-function of formula above in <span class=\"tex-span\"><i>O</i>(1)</span>, you should calculate some additional dp's: </p><p>dp1 — for every basic string, positions inside of them and letter you should calculate leftmost position of current letter that right than current position;</p><p>dp2 — for every element of array of basic strings (it is hyperstring) and letter you should calculate leftmost basic string that have current letter and this string is rinht than current basic string.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ab8527f1ac10b4b4d1feb948447ae95a2a57c78f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a>.</p><p><strong>E div1.</strong> At the first let's try to solve another problem: we have <span class=\"tex-span\"><i>k</i></span> chosed vertices in the tree and we want to find sum of subtree that "spanned" dy them in time <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (with any preprocessing time).</p><p>Let's sort all <span class=\"tex-span\"><i>k</i></span> vertices in order of dfs traversal — <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub></span>, ... , <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>k</i></sub></span>. Consider pathes v1-v2, v2-v3, ... , v(k-1)-vk and vk-v1. You can see that they cover only our requred subtree and every edge is covered exactly two times. So you can just find sum of lengths of these pathes (you can do it in required <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time using LCA algo) and divide obtained value by 2.</p><p>For solving initial problem you should support set of active vertices in ordered state (for example, you can use std::set) and sum of all pathes between all neighbour vertices. Now you can process insert/remove queries in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, and recalculate sum of pathes by finding no more than 3 new pathes also in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d61c652f63078ae0d26fbc9a95899f0f930104b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</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/176\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2</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/181\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2 (Unofficial Div. 2 Edition)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4386\").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: \"4372\",\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=croc-2012-round-2\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-2</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012</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-4386\"><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'>+43</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4386\"><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=\"Apr/20/2012 19:48\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4372#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/4372#comments\">\n 12\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=\"4396\">\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 (10)</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=\"88649\" 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/cholerikasi\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/44515/avatar/782a6a535da57281.jpg'/> </a>\n <div><a href=\"/profile/cholerikasi\" title=\"Specialist cholerikasi\" class=\"rated-user user-cyan\">cholerikasi</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 02:32\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88649\" href=\"?#comment-88649\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"88649\" 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=\"88649\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"44515\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88649\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For problem D (div 2) the formula is slightly incorrect. Correction:</p> <pre><code>dpA[n] = dpA[n-1]*(A-1) + dpB[n-1]*A\ndpB[n] = dpA[n-1]*B + dpB[n-1](B-1)\n</code></pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88649 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88649 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88649\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88932\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PrakharJain\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/27035/avatar/5784d107df6e4a90.jpg'/> </a>\n <div><a href=\"/profile/PrakharJain\" title=\"Candidate Master PrakharJain\" class=\"rated-user user-violet\">PrakharJain</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 00:40\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88932\" href=\"?#comment-88932\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88932\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"27035\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88932\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, you're right.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88932 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88932 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88932\">\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=\"88937\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Ripatti\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 01:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88937\" href=\"?#comment-88937\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88937\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"472\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88937\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you, fixed</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88937 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88937 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88937\">\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=\"88662\" 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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 11:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88662\" href=\"?#comment-88662\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88662\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88662\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In div2 E. Why does the second win when the input is "5 5 1 1 5 4"</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88662 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88662 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88662\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88686\" commentParentId=\"88662\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 15:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88686\" href=\"?#comment-88686\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88662\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88686\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88686\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Brute force proves it</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88686 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88686 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88686\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88688\" commentParentId=\"88686\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 16:01\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88688\" href=\"?#comment-88688\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88686\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88688\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88688\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Did you write the program using brute force and find the regularity before you submit the problem?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88688 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88688 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88688\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88735\" commentParentId=\"88688\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 18:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88735\" href=\"?#comment-88735\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88688\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88735\" 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=\"88735\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88735\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes I am. But I've got Wrong answer on test 9 and then write brute force.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88735 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88735 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88735\">\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=\"249677\" 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/yash_15\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/234147/avatar/2541b99b44dd628f.jpg'/> </a>\n <div><a href=\"/profile/yash_15\" title=\"Expert yash_15\" class=\"rated-user user-blue\">yash_15</a></div>\n </div>\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/06/2015 21:39\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249677\" href=\"?#comment-249677\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249677\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"234147\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249677\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For div 1 B, I want to know that what are values A and B in the recurrence relations? Also I would like to find some AC submissions to this problem.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249677 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249677 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249677\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"313733\" 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/haleyk100198\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a>\n <div><a href=\"/profile/haleyk100198\" title=\"Candidate Master haleyk100198\" class=\"rated-user user-violet\">haleyk100198</a></div>\n </div>\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/07/2016 16:54\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-313733\" href=\"?#comment-313733\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"313733\" 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=\"313733\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"416324\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-313733\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Div1E I have an alternative solution which focuses on binary searching the LCA of a point and a set of points as I didn't noticed that I can double count all necessary path by sorting dfs visiting time.</p><p>Code: <a href=\"//codeforces.com/contest/176/submission/20437271\">http://codeforces.com/contest/176/submission/20437271</a></p><p>(Now reviewing the code, the part of getLCA and sparse table is not required for finding LCA between a point and a set of points)</p><p>The current length of all necessary path is always updated.</p><p>Pre-processing:</p> <ol> <li><p>dfs for finding the visiting time and ending time of each vertex. O(N)</p></li> <li><p>Pre-calculate the binary exponential distance from each vertex to the 2^N parent. O(NlogN)</p></li> </ol><p>The current length of all necessary path is always kept</p><p>Keep a segment tree to check if there are any restored village in a sub-tree in O(logN) time, we will need it for the binary searches for the queries.</p><p>How to handle queries:</p><p>'+': Find two poitns: 1. the LCA of the village being restored with any other already restored villages, 2. the LCA of the new set of points. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>'-': Find two points: 1. the LCA of the remaining set, 2. the LCA of the village being destroyed with any other villages that are still available. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>Remember to handle cases where the restored villages set size if smaller than 2.</p><p>'?': Just return the length value, this can be done in O(1) time.</p><p>Total time complexity: O(NlogN + qlogN * logN), which is slightly worse than the intended solution but it still fits in the TL very easily.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-313733 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-313733 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-313733\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"713689\" 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/gabaswillwinIOI2022\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/gabaswillwinIOI2022\" title=\"Master gabaswillwinIOI2022\" class=\"rated-user user-orange\">gabaswillwinIOI2022</a></div>\n </div>\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/23/2020 14:32\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-713689\" href=\"?#comment-713689\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"713689\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1567470\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-713689\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>O(|w| + logk) solution for <a href=\"/contest/176/problem/B\" title=\"Croc Champ 2012 - Round 2\">176B - Word Cut</a> (Div 1 B) <a href=\"/contest/176/submission/96438522\" title=\"Submission 96438522 by gabaswillwinIOI2022\">96438522</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-713689 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-713689 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-713689\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4396\" 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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Archaeology"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Archaeology</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>This time you should help a team of researchers on an island in the Pacific Ocean. They research the culture of the ancient tribes that used to inhabit the island many years ago.</p><p>Overall they've dug out <span class=\"tex-span\"><i>n</i></span> villages. Some pairs of villages were connected by roads. People could go on the roads in both directions. Overall there were exactly <span class=\"tex-span\"><i>n</i> - 1</span> roads, and from any village one could get to any other one.</p><p>The tribes were not peaceful and they had many wars. As a result of the wars, some villages were destroyed completely. During more peaceful years some of the villages were restored.</p><p>At each moment of time people <span class=\"tex-font-style-underline\">used</span> only those roads that belonged to some shortest way between two villages <span class=\"tex-font-style-underline\">that existed at the given moment</span>. In other words, people used the minimum subset of roads in such a way, that it was possible to get from any existing village to any other existing one. Note that throughout the island's whole history, there existed exactly <span class=\"tex-span\"><i>n</i> - 1</span> roads that have been found by the researchers. There never were any other roads.</p><p>The researchers think that observing the total sum of used roads’ lengths at different moments of time can help to better understand the tribes' culture and answer several historical questions.</p><p>You will be given the full history of the tribes' existence. Your task is to determine the total length of used roads at some moments of time.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of villages. The next <span class=\"tex-span\"><i>n</i> - 1</span> lines describe the roads. The <span class=\"tex-span\"><i>i</i></span>-th of these lines contains three integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>c</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>, <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>c</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i></span>) — the numbers of villages that are connected by the <span class=\"tex-span\"><i>i</i></span>-th road and the road's length. The numbers in the lines are separated by a space.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> (<span class=\"tex-span\">1 ≤ <i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of queries. Then follow <span class=\"tex-span\"><i>q</i></span> queries, one per line, ordered by time. Each query belongs to one of three types:</p><ul><li> \"<span class=\"tex-font-style-tt\">+ </span><span class=\"tex-span\"><i>x</i></span>\" — village number <span class=\"tex-span\"><i>x</i></span> is restored (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ <i>n</i></span>). </li><li> \"<span class=\"tex-font-style-tt\">- </span><span class=\"tex-span\"><i>x</i></span>\" — village number <span class=\"tex-span\"><i>x</i></span> is destroyed (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ <i>n</i></span>). </li><li> \"<span class=\"tex-font-style-tt\">?</span>\" — the archaeologists want to know the total length of the roads which were used for that time period.</li></ul><p>It is guaranteed that the queries do not contradict each other, that is, there won't be queries to destroy non-existing villages or restore the already existing ones. It is guaranteed that we have at least one query of type \"<span class=\"tex-font-style-tt\">?</span>\". It is also guaranteed that one can get from any village to any other one by the given roads.</p><p>At the initial moment of time no village is considered to exist.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each query of type \"<span class=\"tex-font-style-tt\">?</span>\" print the total length of used roads on a single line. You should print the answers to the queries in the order, in which they 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 <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>6<br/>1 2 1<br/>1 3 5<br/>4 1 7<br/>4 5 3<br/>6 4 2<br/>10<br/>+ 3<br/>+ 1<br/>?<br/>+ 6<br/>?<br/>+ 5<br/>?<br/>- 6<br/>- 3<br/>?<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/>14<br/>17<br/>10<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=\"7ba9819ffeb3403d047236b624d525b4\"/>\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=\"19756bd4dfb417b7c391f4abee7fa342560c6bd4\"/>\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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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_78add99a77cc93015706bc41d08856844b680120\">\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. Archaeology</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>This time you should help a team of researchers on an island in the Pacific Ocean. They research the culture of the ancient tribes that used to inhabit the island many years ago.</p><p>Overall they've dug out <span class=\"tex-span\"><i>n</i></span> villages. Some pairs of villages were connected by roads. People could go on the roads in both directions. Overall there were exactly <span class=\"tex-span\"><i>n</i> - 1</span> roads, and from any village one could get to any other one.</p><p>The tribes were not peaceful and they had many wars. As a result of the wars, some villages were destroyed completely. During more peaceful years some of the villages were restored.</p><p>At each moment of time people <span class=\"tex-font-style-underline\">used</span> only those roads that belonged to some shortest way between two villages <span class=\"tex-font-style-underline\">that existed at the given moment</span>. In other words, people used the minimum subset of roads in such a way, that it was possible to get from any existing village to any other existing one. Note that throughout the island's whole history, there existed exactly <span class=\"tex-span\"><i>n</i> - 1</span> roads that have been found by the researchers. There never were any other roads.</p><p>The researchers think that observing the total sum of used roads’ lengths at different moments of time can help to better understand the tribes' culture and answer several historical questions.</p><p>You will be given the full history of the tribes' existence. Your task is to determine the total length of used roads at some moments of time.</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> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of villages. The next <span class=\"tex-span\"><i>n</i> - 1</span> lines describe the roads. The <span class=\"tex-span\"><i>i</i></span>-th of these lines contains three integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>c</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>, <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>c</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i></span>) — the numbers of villages that are connected by the <span class=\"tex-span\"><i>i</i></span>-th road and the road's length. The numbers in the lines are separated by a space.</p><p>The next line contains an integer <span class=\"tex-span\"><i>q</i></span> (<span class=\"tex-span\">1 ≤ <i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of queries. Then follow <span class=\"tex-span\"><i>q</i></span> queries, one per line, ordered by time. Each query belongs to one of three types:</p><ul><li> "<span class=\"tex-font-style-tt\">+ </span><span class=\"tex-span\"><i>x</i></span>" — village number <span class=\"tex-span\"><i>x</i></span> is restored (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ <i>n</i></span>). </li><li> "<span class=\"tex-font-style-tt\">- </span><span class=\"tex-span\"><i>x</i></span>" — village number <span class=\"tex-span\"><i>x</i></span> is destroyed (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ <i>n</i></span>). </li><li> "<span class=\"tex-font-style-tt\">?</span>" — the archaeologists want to know the total length of the roads which were used for that time period.</li></ul><p>It is guaranteed that the queries do not contradict each other, that is, there won't be queries to destroy non-existing villages or restore the already existing ones. It is guaranteed that we have at least one query of type "<span class=\"tex-font-style-tt\">?</span>". It is also guaranteed that one can get from any village to any other one by the given roads.</p><p>At the initial moment of time no village is considered to exist.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each query of type "<span class=\"tex-font-style-tt\">?</span>" print the total length of used roads on a single line. You should print the answers to the queries in the order, in which they 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 <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>6<br />1 2 1<br />1 3 5<br />4 1 7<br />4 5 3<br />6 4 2<br />10<br />+ 3<br />+ 1<br />?<br />+ 6<br />?<br />+ 5<br />?<br />- 6<br />- 3<br />?<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br />14<br />17<br />10<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 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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='15679b166c86ee80065b195f1dc12b4b'/>\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)\" 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/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=\"4386\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4372\"> <p>Croc Champ 2012 — Round 2 — Editorial</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=\"Apr/20/2012 19:48\">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>A div2.</strong> Required row is row that have only one star inside. Requred column is comumn that also have only one star inside. So, you can iterate over all rows/columns, calculate number of stars inside them and find the answer.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> .</p><p><strong>B div2.</strong> Naive solution <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span> (where you check all triplets) doesn't fin into time limits.</p><p>You can see that for every two points from triplet (for example, for A and C) you can find place of the third point. So you can find number of requred triplets just inerate over all pairs of points and check middle point between points in every pair.</p><p>How to fast check position? You can add 1000 for all coordinates (you can see that this operation doesn't change the answer) and mark them in the 2-dimensional boolean array 2001х2001. So you can check every position for point in <span class=\"tex-span\"><i>O</i>(1)</span> time.</p><p>Obtained solution works in <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>Authors are <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>, <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a></p><p><strong>A div1. C div2.</strong> In this problem some greedy solution expected.</p><p>Let fix 2 planets: in planet i we will buy items, in planet j we will sell the ones. <em>Profit of item</em> of type k will be b_jk-a_ik. Every item has size 1, so you should greedy take items in order of decreasing of profits of items while you have place in the hold.</p><p>Scheme of full solution: you should iterate over all pairs of planet, for every pair greedy take items and find total profit. At the end you should find maximal total profit over all pairs and output it.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>B div1. D div2.</strong> You can see that split oparetion is just cyclically shift of string. You can go from any cyclically shift to any other one except the current one.</p><p>Let's call some cyclically shift <em>good</em> iff it equal to the final string. All others cyclically shifts we will call <em>bad</em>. You can check all shifts in <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup>)</span> time. Let's you have A good shifts and B bad ones.</p><p>Let's define dpA[n] as number of ways to get some good shift using n splits and за dpB[n] as number of ways to get some bad shift using n splits.</p><p>dpA[0]=1, dpB[0]=0 or dpA[0]=0, dpB[0]=1 according to the first shift is good or not. All other values of dp you can get using following reccurences:</p><p>dpA[n] = dpA[n-1] * (A-1) + dpB[n-1] * A</p><p>dpB[n] = dpA[n-1] * B + dpB[n-1] * (B-1)</p><p>Answer will be dpA[k]. So you have <span class=\"tex-span\"><i>O</i>(|<i>w</i>|<sup class=\"upper-index\">2</sup> + <i>k</i>)</span> solution.</p><p>Also this problem can be solved in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/30663b28627443a73b3aed1e96e06b64506cfc8e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a></p><p><strong>C div1. E div2.</strong> The second player have easy strategy to hold some chip in position <span class=\"tex-span\">(<i>X</i>, <i>Y</i>)</span> in one of four half-planes — <span class=\"tex-span\"><i>x</i> ≤ <i>X</i> + 2</span>, <span class=\"tex-span\"><i>x</i> ≥ <i>X</i> - 2</span>, <span class=\"tex-span\"><i>y</i> ≤ <i>Y</i> + 2</span> и <span class=\"tex-span\"><i>y</i> ≥ <i>Y</i> - 2</span>. He can chose one of these half-planes by himself.</p><p>So, in case <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) > 4</span> the second player wins — he just holds chips in half-planes that have no common cells.</p><p>Cases for <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> expected to solve using some bruteforce. You can see that moving chips in way of distancing from each other is not profitable for the first player. Therefore you can bruteforce the game in square no more than <span class=\"tex-span\">5 × 5</span>. If your bruteforce so slow and doesn't fit into 2 sec, you can use precalculation. Also you can write some dp using masks.</p><p>Also you can check cases <span class=\"tex-span\"><i>max</i>(|<i>x</i>1 - <i>x</i>2|, |<i>y</i>1 - <i>y</i>2|) ≤ 4</span> by hand. But there you can easy make some mistakes.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>D div1.</strong> Let's define <span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>]</span> as the minimal prefix of hyperstring that have with prefix of <span class=\"tex-span\"><i>t</i></span> of length <span class=\"tex-span\"><i>len</i></span> largest common sequence of length <span class=\"tex-span\"><i>len</i></span>.</p><p>Then you have see reccurences:</p><p><span class=\"tex-span\"><i>dp</i>[<i>pre</i>][<i>len</i>] = <i>min</i>(<i>dp</i>[<i>pre</i> - 1][<i>len</i>], </span> leftmost position of letter <span class=\"tex-span\"><i>s</i>[<i>pre</i>]</span> in <span class=\"tex-span\"><i>t</i></span> that right than <span class=\"tex-span\"><i>dp</i>[<i>pre</i> - 1][<i>len</i> - 1])</span>.</p><p>For finding value of the second part inside min-function of formula above in <span class=\"tex-span\"><i>O</i>(1)</span>, you should calculate some additional dp's: </p><p>dp1 — for every basic string, positions inside of them and letter you should calculate leftmost position of current letter that right than current position;</p><p>dp2 — for every element of array of basic strings (it is hyperstring) and letter you should calculate leftmost basic string that have current letter and this string is rinht than current basic string.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ab8527f1ac10b4b4d1feb948447ae95a2a57c78f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/havaliza\" title=\"Candidate Master havaliza\">havaliza</a>.</p><p><strong>E div1.</strong> At the first let's try to solve another problem: we have <span class=\"tex-span\"><i>k</i></span> chosed vertices in the tree and we want to find sum of subtree that "spanned" dy them in time <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> (with any preprocessing time).</p><p>Let's sort all <span class=\"tex-span\"><i>k</i></span> vertices in order of dfs traversal — <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub></span>, ... , <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>k</i></sub></span>. Consider pathes v1-v2, v2-v3, ... , v(k-1)-vk and vk-v1. You can see that they cover only our requred subtree and every edge is covered exactly two times. So you can just find sum of lengths of these pathes (you can do it in required <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c0d62c767dafab57b63df9b87e9e6cddbdfbe51.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> time using LCA algo) and divide obtained value by 2.</p><p>For solving initial problem you should support set of active vertices in ordered state (for example, you can use std::set) and sum of all pathes between all neighbour vertices. Now you can process insert/remove queries in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, and recalculate sum of pathes by finding no more than 3 new pathes also in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/21cdfc8587975fb007b82c9da4f34241b79b0d6c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>So you have <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d61c652f63078ae0d26fbc9a95899f0f930104b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> solution.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</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/176\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2</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/181\" class=\"notice\" style=\"text-decoration: none;\">Croc Champ 2012 - Round 2 (Unofficial Div. 2 Edition)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4386\").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: \"4372\",\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=croc-2012-round-2\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012-round-2</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 <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=croc-2012\" class=\"tag notice\" style=\"text-decoration: none;\">croc-2012</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-4386\"><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'>+43</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4386\"><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=\"Apr/20/2012 19:48\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4372#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/4372#comments\">\n 12\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=\"4396\">\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 (10)</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=\"88649\" 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/cholerikasi\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/44515/avatar/782a6a535da57281.jpg'/> </a>\n <div><a href=\"/profile/cholerikasi\" title=\"Specialist cholerikasi\" class=\"rated-user user-cyan\">cholerikasi</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 02:32\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88649\" href=\"?#comment-88649\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"88649\" 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=\"88649\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"44515\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88649\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For problem D (div 2) the formula is slightly incorrect. Correction:</p> <pre><code>dpA[n] = dpA[n-1]*(A-1) + dpB[n-1]*A\ndpB[n] = dpA[n-1]*B + dpB[n-1](B-1)\n</code></pre></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88649 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88649 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88649\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88932\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PrakharJain\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/27035/avatar/5784d107df6e4a90.jpg'/> </a>\n <div><a href=\"/profile/PrakharJain\" title=\"Candidate Master PrakharJain\" class=\"rated-user user-violet\">PrakharJain</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 00:40\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88932\" href=\"?#comment-88932\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88932\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"27035\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88932\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes, you're right.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88932 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88932 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88932\">\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=\"88937\" commentParentId=\"88649\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Ripatti\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/22/2012 01:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88937\" href=\"?#comment-88937\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88649\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88937\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"472\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88937\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thank you, fixed</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88937 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88937 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88937\">\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=\"88662\" 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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 11:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88662\" href=\"?#comment-88662\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88662\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88662\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In div2 E. Why does the second win when the input is "5 5 1 1 5 4"</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88662 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88662 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88662\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88686\" commentParentId=\"88662\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 15:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88686\" href=\"?#comment-88686\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88662\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88686\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88686\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Brute force proves it</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88686 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88686 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88686\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88688\" commentParentId=\"88686\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/1292765944\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/1292765944\" title=\"Expert 1292765944\" class=\"rated-user user-blue\">1292765944</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 16:01\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88688\" href=\"?#comment-88688\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88686\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"88688\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"23637\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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-88688\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Did you write the program using brute force and find the regularity before you submit the problem?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88688 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88688 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88688\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"88735\" commentParentId=\"88688\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\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/Edvard\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/345/avatar/b5fe685881b67116.jpg'/> </a>\n <div><a href=\"/profile/Edvard\" title=\"Candidate Master Edvard\" class=\"rated-user user-violet\">Edvard</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/21/2012 18:57\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-88735\" href=\"?#comment-88735\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-88688\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</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=\"88735\" 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=\"88735\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"345\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-88735\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Yes I am. But I've got Wrong answer on test 9 and then write brute force.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-88735 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-88735 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-88735\">\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=\"249677\" 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/yash_15\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/234147/avatar/2541b99b44dd628f.jpg'/> </a>\n <div><a href=\"/profile/yash_15\" title=\"Expert yash_15\" class=\"rated-user user-blue\">yash_15</a></div>\n </div>\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/06/2015 21:39\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249677\" href=\"?#comment-249677\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249677\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"234147\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249677\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For div 1 B, I want to know that what are values A and B in the recurrence relations? Also I would like to find some AC submissions to this problem.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249677 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249677 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249677\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"313733\" 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/haleyk100198\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a>\n <div><a href=\"/profile/haleyk100198\" title=\"Candidate Master haleyk100198\" class=\"rated-user user-violet\">haleyk100198</a></div>\n </div>\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/07/2016 16:54\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-313733\" href=\"?#comment-313733\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</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=\"313733\" 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=\"313733\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-10\"\r\n data-commentUserId=\"416324\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-10</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-313733\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For Div1E I have an alternative solution which focuses on binary searching the LCA of a point and a set of points as I didn't noticed that I can double count all necessary path by sorting dfs visiting time.</p><p>Code: <a href=\"//codeforces.com/contest/176/submission/20437271\">http://codeforces.com/contest/176/submission/20437271</a></p><p>(Now reviewing the code, the part of getLCA and sparse table is not required for finding LCA between a point and a set of points)</p><p>The current length of all necessary path is always updated.</p><p>Pre-processing:</p> <ol> <li><p>dfs for finding the visiting time and ending time of each vertex. O(N)</p></li> <li><p>Pre-calculate the binary exponential distance from each vertex to the 2^N parent. O(NlogN)</p></li> </ol><p>The current length of all necessary path is always kept</p><p>Keep a segment tree to check if there are any restored village in a sub-tree in O(logN) time, we will need it for the binary searches for the queries.</p><p>How to handle queries:</p><p>'+': Find two poitns: 1. the LCA of the village being restored with any other already restored villages, 2. the LCA of the new set of points. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>'-': Find two points: 1. the LCA of the remaining set, 2. the LCA of the village being destroyed with any other villages that are still available. Update the LCA of all villages if necessary. This can be done in O(logN * logN) time.</p><p>Remember to handle cases where the restored villages set size if smaller than 2.</p><p>'?': Just return the length value, this can be done in O(1) time.</p><p>Total time complexity: O(NlogN + qlogN * logN), which is slightly worse than the intended solution but it still fits in the TL very easily.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-313733 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-313733 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-313733\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"713689\" 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/gabaswillwinIOI2022\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/gabaswillwinIOI2022\" title=\"Master gabaswillwinIOI2022\" class=\"rated-user user-orange\">gabaswillwinIOI2022</a></div>\n </div>\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/23/2020 14:32\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-713689\" href=\"?#comment-713689\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"713689\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1567470\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-713689\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>O(|w| + logk) solution for <a href=\"/contest/176/problem/B\" title=\"Croc Champ 2012 - Round 2\">176B - Word Cut</a> (Div 1 B) <a href=\"/contest/176/submission/96438522\" title=\"Submission 96438522 by gabaswillwinIOI2022\">96438522</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-713689 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-713689 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-713689\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4396\" 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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Good Matrix Elements"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A1. Good Matrix Elements</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 Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an <span class=\"tex-span\"><i>n</i> × <i>n</i></span> size matrix, where <span class=\"tex-span\"><i>n</i></span> is odd. The Smart Beaver considers the following matrix elements good: </p><ul> <li> Elements of the main diagonal. </li><li> Elements of the secondary diagonal. </li><li> Elements of the \"middle\" row — the row which has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> rows above it and the same number of rows below it. </li><li> Elements of the \"middle\" column — the column that has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> columns to the left of it and the same number of columns to the right of it. </li></ul><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d97d5d0d20c81a6225574d6cf14041964615f693.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> The figure shows a <span class=\"tex-span\">5 × 5</span> matrix. The good elements are marked with green. </span> </center><p>Help the Smart Beaver count the sum of good elements of the given matrix.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input data contains a single odd integer <span class=\"tex-span\"><i>n</i></span>. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> <span class=\"tex-span\">(0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100)</span> separated by single spaces — the elements of the given matrix.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul><p>The input limitations for getting 100 points are:</p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 101</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the sum of good matrix elements.</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/>4 5 6<br/>7 8 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>45<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample all matrix elements will be good. 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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A1. Good Matrix Elements</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 Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an <span class=\"tex-span\"><i>n</i> × <i>n</i></span> size matrix, where <span class=\"tex-span\"><i>n</i></span> is odd. The Smart Beaver considers the following matrix elements good: </p><ul> <li> Elements of the main diagonal. </li><li> Elements of the secondary diagonal. </li><li> Elements of the "middle" row — the row which has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows above it and the same number of rows below it. </li><li> Elements of the "middle" column — the column that has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> columns to the left of it and the same number of columns to the right of it. </li></ul><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d97d5d0d20c81a6225574d6cf14041964615f693.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> The figure shows a <span class=\"tex-span\">5 × 5</span> matrix. The good elements are marked with green. </span> </center><p>Help the Smart Beaver count the sum of good elements of the given matrix.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input data contains a single odd integer <span class=\"tex-span\"><i>n</i></span>. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> <span class=\"tex-span\">(0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100)</span> separated by single spaces — the elements of the given matrix.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul><p>The input limitations for getting 100 points are:</p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 101</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the sum of good matrix elements.</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 />4 5 6<br />7 8 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>45<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample all matrix elements will be good. 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Good Matrix Elements"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A2. Good Matrix Elements</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 Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an <span class=\"tex-span\"><i>n</i> × <i>n</i></span> size matrix, where <span class=\"tex-span\"><i>n</i></span> is odd. The Smart Beaver considers the following matrix elements good: </p><ul> <li> Elements of the main diagonal. </li><li> Elements of the secondary diagonal. </li><li> Elements of the \"middle\" row — the row which has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> rows above it and the same number of rows below it. </li><li> Elements of the \"middle\" column — the column that has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> columns to the left of it and the same number of columns to the right of it. </li></ul><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d97d5d0d20c81a6225574d6cf14041964615f693.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> The figure shows a <span class=\"tex-span\">5 × 5</span> matrix. The good elements are marked with green. </span> </center><p>Help the Smart Beaver count the sum of good elements of the given matrix.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input data contains a single odd integer <span class=\"tex-span\"><i>n</i></span>. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> <span class=\"tex-span\">(0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100)</span> separated by single spaces — the elements of the given matrix.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul><p>The input limitations for getting 100 points are:</p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 101</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the sum of good matrix elements.</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/>4 5 6<br/>7 8 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>45<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/>1 1 1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample all matrix elements will be good. 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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A2. Good Matrix Elements</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 Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an <span class=\"tex-span\"><i>n</i> × <i>n</i></span> size matrix, where <span class=\"tex-span\"><i>n</i></span> is odd. The Smart Beaver considers the following matrix elements good: </p><ul> <li> Elements of the main diagonal. </li><li> Elements of the secondary diagonal. </li><li> Elements of the "middle" row — the row which has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows above it and the same number of rows below it. </li><li> Elements of the "middle" column — the column that has exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/55e8f30a55c1086f22e41e6036894dfd3c68d3a3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> columns to the left of it and the same number of columns to the right of it. </li></ul><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d97d5d0d20c81a6225574d6cf14041964615f693.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> The figure shows a <span class=\"tex-span\">5 × 5</span> matrix. The good elements are marked with green. </span> </center><p>Help the Smart Beaver count the sum of good elements of the given matrix.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input data contains a single odd integer <span class=\"tex-span\"><i>n</i></span>. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> <span class=\"tex-span\">(0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100)</span> separated by single spaces — the elements of the given matrix.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul><p>The input limitations for getting 100 points are:</p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 101</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the sum of good matrix elements.</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 />4 5 6<br />7 8 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>45<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br />1 1 1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample all matrix elements will be good. 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Rectangular Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B1. Rectangular 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>The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has <span class=\"tex-span\"><i>n</i></span> pebbles. He arranges them in <span class=\"tex-span\"><i>a</i></span> equal rows, each row has <span class=\"tex-span\"><i>b</i></span> pebbles (<span class=\"tex-span\"><i>a</i> > 1</span>). Note that the Beaver must use all the pebbles he has, i. e. <span class=\"tex-span\"><i>n</i> = <i>a</i>·<i>b</i></span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/7f4dd23a2a6cd8290d060773328f7811098a6a8a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> 10 pebbles are arranged in two rows, each row has 5 pebbles </span> </center><p>Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, <span class=\"tex-span\"><i>b</i></span> pebbles) and discards all other pebbles. Then he arranges <span class=\"tex-font-style-bf\">all</span> his pebbles again (possibly choosing other values of <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. </p><p>The game process can be represented as a finite sequence of integers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>k</i></sub></span>, where: </p><ul> <li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = <i>n</i></span> </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> is the number of pebbles that the Beaver ends up with after the <span class=\"tex-span\"><i>i</i></span>-th move, that is, the number of pebbles in a row after some arrangement of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> pebbles (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>k</i></span>). Note that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub> > <i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>. </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>k</i></sub> = 1</span> </li></ul><p>The result of the game is the sum of numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>. You are given <span class=\"tex-span\"><i>n</i></span>. Find the maximum possible result of the game.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains a single integer <span class=\"tex-span\"><i>n</i></span> — the initial number of pebbles the Smart Beaver has.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 50</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum possible result of the game.</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<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>8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Consider the first example (<span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = 10</span>). The possible options for the game development are:</p><ul> <li> Arrange the pebbles in 10 rows, one pebble per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 1</span>, and the game ends after the first move with the result of 11. </li><li> Arrange the pebbles in 5 rows, two pebbles per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 2</span>, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 13. </li><li> Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 5, <i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 16 — the maximum possible result. </li></ul></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=\"2fc98613256310a5911cf4f9b74a34ee\"/>\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 - B1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B1. Rectangular 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>The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has <span class=\"tex-span\"><i>n</i></span> pebbles. He arranges them in <span class=\"tex-span\"><i>a</i></span> equal rows, each row has <span class=\"tex-span\"><i>b</i></span> pebbles (<span class=\"tex-span\"><i>a</i> > 1</span>). Note that the Beaver must use all the pebbles he has, i. e. <span class=\"tex-span\"><i>n</i> = <i>a</i>·<i>b</i></span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/7f4dd23a2a6cd8290d060773328f7811098a6a8a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> 10 pebbles are arranged in two rows, each row has 5 pebbles </span> </center><p>Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, <span class=\"tex-span\"><i>b</i></span> pebbles) and discards all other pebbles. Then he arranges <span class=\"tex-font-style-bf\">all</span> his pebbles again (possibly choosing other values of <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. </p><p>The game process can be represented as a finite sequence of integers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>k</i></sub></span>, where: </p><ul> <li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = <i>n</i></span> </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> is the number of pebbles that the Beaver ends up with after the <span class=\"tex-span\"><i>i</i></span>-th move, that is, the number of pebbles in a row after some arrangement of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> pebbles (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>k</i></span>). Note that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub> > <i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>. </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>k</i></sub> = 1</span> </li></ul><p>The result of the game is the sum of numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>. You are given <span class=\"tex-span\"><i>n</i></span>. Find the maximum possible result of the game.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains a single integer <span class=\"tex-span\"><i>n</i></span> — the initial number of pebbles the Smart Beaver has.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 50</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum possible result of the game.</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<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>8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Consider the first example (<span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = 10</span>). The possible options for the game development are:</p><ul> <li> Arrange the pebbles in 10 rows, one pebble per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 1</span>, and the game ends after the first move with the result of 11. </li><li> Arrange the pebbles in 5 rows, two pebbles per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 2</span>, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 13. </li><li> Finally, arrange the pebbles in two rows, five pebbles per row. 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Rectangular Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B2. Rectangular 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>The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has <span class=\"tex-span\"><i>n</i></span> pebbles. He arranges them in <span class=\"tex-span\"><i>a</i></span> equal rows, each row has <span class=\"tex-span\"><i>b</i></span> pebbles (<span class=\"tex-span\"><i>a</i> > 1</span>). Note that the Beaver must use all the pebbles he has, i. e. <span class=\"tex-span\"><i>n</i> = <i>a</i>·<i>b</i></span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/7f4dd23a2a6cd8290d060773328f7811098a6a8a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> 10 pebbles are arranged in two rows, each row has 5 pebbles </span> </center><p>Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, <span class=\"tex-span\"><i>b</i></span> pebbles) and discards all other pebbles. Then he arranges <span class=\"tex-font-style-bf\">all</span> his pebbles again (possibly choosing other values of <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. </p><p>The game process can be represented as a finite sequence of integers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>k</i></sub></span>, where: </p><ul> <li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = <i>n</i></span> </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> is the number of pebbles that the Beaver ends up with after the <span class=\"tex-span\"><i>i</i></span>-th move, that is, the number of pebbles in a row after some arrangement of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> pebbles (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>k</i></span>). Note that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub> > <i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>. </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>k</i></sub> = 1</span> </li></ul><p>The result of the game is the sum of numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>. You are given <span class=\"tex-span\"><i>n</i></span>. Find the maximum possible result of the game.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains a single integer <span class=\"tex-span\"><i>n</i></span> — the initial number of pebbles the Smart Beaver has.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 50</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum possible result of the game.</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<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>8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Consider the first example (<span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = 10</span>). The possible options for the game development are:</p><ul> <li> Arrange the pebbles in 10 rows, one pebble per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 1</span>, and the game ends after the first move with the result of 11. </li><li> Arrange the pebbles in 5 rows, two pebbles per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 2</span>, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 13. </li><li> Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 5, <i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 16 — the maximum possible result. </li></ul></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=\"fea6eca23b997a6933eda8d38c0cedb0\"/>\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 - B2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B2. Rectangular 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>The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has <span class=\"tex-span\"><i>n</i></span> pebbles. He arranges them in <span class=\"tex-span\"><i>a</i></span> equal rows, each row has <span class=\"tex-span\"><i>b</i></span> pebbles (<span class=\"tex-span\"><i>a</i> > 1</span>). Note that the Beaver must use all the pebbles he has, i. e. <span class=\"tex-span\"><i>n</i> = <i>a</i>·<i>b</i></span>.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/7f4dd23a2a6cd8290d060773328f7811098a6a8a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> 10 pebbles are arranged in two rows, each row has 5 pebbles </span> </center><p>Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, <span class=\"tex-span\"><i>b</i></span> pebbles) and discards all other pebbles. Then he arranges <span class=\"tex-font-style-bf\">all</span> his pebbles again (possibly choosing other values of <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span>) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. </p><p>The game process can be represented as a finite sequence of integers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub>, ..., <i>c</i><sub class=\"lower-index\"><i>k</i></sub></span>, where: </p><ul> <li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = <i>n</i></span> </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> is the number of pebbles that the Beaver ends up with after the <span class=\"tex-span\"><i>i</i></span>-th move, that is, the number of pebbles in a row after some arrangement of <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span> pebbles (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>k</i></span>). Note that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub> > <i>c</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span>. </li><li> <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>k</i></sub> = 1</span> </li></ul><p>The result of the game is the sum of numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>i</i></sub></span>. You are given <span class=\"tex-span\"><i>n</i></span>. Find the maximum possible result of the game.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line of the input contains a single integer <span class=\"tex-span\"><i>n</i></span> — the initial number of pebbles the Smart Beaver has.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 50</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum possible result of the game.</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<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>8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Consider the first example (<span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub> = 10</span>). The possible options for the game development are:</p><ul> <li> Arrange the pebbles in 10 rows, one pebble per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 1</span>, and the game ends after the first move with the result of 11. </li><li> Arrange the pebbles in 5 rows, two pebbles per row. Then <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub> = 2</span>, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub> = 1</span>, and the game ends with the result of 13. </li><li> Finally, arrange the pebbles in two rows, five pebbles per row. 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Party"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C1. Party</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>To celebrate the second ABBYY Cup tournament, the Smart Beaver decided to throw a party. The Beaver has a lot of acquaintances, some of them are friends with each other, and some of them dislike each other. To make party successful, the Smart Beaver wants to invite only those of his friends who are connected by friendship relations, and not to invite those who dislike each other. Both friendship and dislike are mutual feelings.</p><p>More formally, for each invited person the following conditions should be fulfilled: </p><ul> <li> all his friends should also be invited to the party; </li><li> the party shouldn't have any people he dislikes; </li><li> all people who are invited to the party should be connected with him by friendship either directly or through a chain of common friends of arbitrary length. We'll say that people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i></sub></span> are connected through a chain of common friends if there exists a sequence of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>p</i> - 1</sub></span> such that all pairs of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>p</i></span>) are friends. </li></ul><p>Help the Beaver find the maximum number of acquaintances he can invite.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains an integer <span class=\"tex-span\"><i>n</i></span> — the number of the Beaver's acquaintances. </p><p>The second line contains an integer <span class=\"tex-span\"><i>k</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4723a08673d63c25b651f89d58d47e46a4430ea9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — the number of pairs of friends. Next <span class=\"tex-span\"><i>k</i></span> lines contain space-separated pairs of 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> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/447b0a18d2967dc78efba89fef879ac76d26c94a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — indices of people who form the <span class=\"tex-span\"><i>i</i></span>-th pair of friends.</p><p>The next line contains an integer <span class=\"tex-span\"><i>m</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c1e79cb16ccc4416463a48018b8621e92ff2f48.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — the number of pairs of people who dislike each other. Next <span class=\"tex-span\"><i>m</i></span> lines describe pairs of people who dislike each other in the same format as the pairs of friends were described.</p><p>Each pair of people is mentioned in the input at most once <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a7d2d374a0c2f92f490cea488df2d83503da07b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. In particular, two persons cannot be friends and dislike each other at the same time.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 14</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 2000</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output a single number — the maximum number of people that can be invited to the party. If a group of people that meets all the requirements is impossible to select, output 0.</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>9<br/>8<br/>1 2<br/>1 3<br/>2 3<br/>4 5<br/>6 7<br/>7 8<br/>8 9<br/>9 6<br/>2<br/>1 6<br/>7 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's have a look at the example. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a592ed9e35f21072bf632be91d9156aa29dd0198.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>Two groups of people can be invited: <span class=\"tex-span\">{1, 2, 3}</span> and <span class=\"tex-span\">{4, 5}</span>, thus the answer will be the size of the largest of these groups. Group <span class=\"tex-span\">{6, 7, 8, 9}</span> doesn't fit, since it includes people <span class=\"tex-span\">7</span> and <span class=\"tex-span\">9</span> who dislike each other. Group <span class=\"tex-span\">{1, 2, 3, 4, 5}</span> also doesn't fit, because not all of its members are connected by a chain of common friends (for example, people <span class=\"tex-span\">2</span> and <span class=\"tex-span\">5</span> aren't connected).</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=\"d76936a275bb130bb180f52061ac580c\"/>\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 - C1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C1 - 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=\"C1\" data-uuid=\"ps_e37677dda83eb4d4d86c81d723445452df8f5837\">\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\">C1. Party</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>To celebrate the second ABBYY Cup tournament, the Smart Beaver decided to throw a party. The Beaver has a lot of acquaintances, some of them are friends with each other, and some of them dislike each other. To make party successful, the Smart Beaver wants to invite only those of his friends who are connected by friendship relations, and not to invite those who dislike each other. Both friendship and dislike are mutual feelings.</p><p>More formally, for each invited person the following conditions should be fulfilled: </p><ul> <li> all his friends should also be invited to the party; </li><li> the party shouldn't have any people he dislikes; </li><li> all people who are invited to the party should be connected with him by friendship either directly or through a chain of common friends of arbitrary length. We'll say that people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i></sub></span> are connected through a chain of common friends if there exists a sequence of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>p</i> - 1</sub></span> such that all pairs of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>p</i></span>) are friends. </li></ul><p>Help the Beaver find the maximum number of acquaintances he can invite.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains an integer <span class=\"tex-span\"><i>n</i></span> — the number of the Beaver's acquaintances. </p><p>The second line contains an integer <span class=\"tex-span\"><i>k</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4723a08673d63c25b651f89d58d47e46a4430ea9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — the number of pairs of friends. Next <span class=\"tex-span\"><i>k</i></span> lines contain space-separated pairs of 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> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/447b0a18d2967dc78efba89fef879ac76d26c94a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — indices of people who form the <span class=\"tex-span\"><i>i</i></span>-th pair of friends.</p><p>The next line contains an integer <span class=\"tex-span\"><i>m</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c1e79cb16ccc4416463a48018b8621e92ff2f48.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — the number of pairs of people who dislike each other. Next <span class=\"tex-span\"><i>m</i></span> lines describe pairs of people who dislike each other in the same format as the pairs of friends were described.</p><p>Each pair of people is mentioned in the input at most once <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a7d2d374a0c2f92f490cea488df2d83503da07b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In particular, two persons cannot be friends and dislike each other at the same time.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 14</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 2000</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output a single number — the maximum number of people that can be invited to the party. If a group of people that meets all the requirements is impossible to select, output 0.</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>9<br />8<br />1 2<br />1 3<br />2 3<br />4 5<br />6 7<br />7 8<br />8 9<br />9 6<br />2<br />1 6<br />7 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's have a look at the example. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a592ed9e35f21072bf632be91d9156aa29dd0198.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>Two groups of people can be invited: <span class=\"tex-span\">{1, 2, 3}</span> and <span class=\"tex-span\">{4, 5}</span>, thus the answer will be the size of the largest of these groups. Group <span class=\"tex-span\">{6, 7, 8, 9}</span> doesn't fit, since it includes people <span class=\"tex-span\">7</span> and <span class=\"tex-span\">9</span> who dislike each other. Group <span class=\"tex-span\">{1, 2, 3, 4, 5}</span> also doesn't fit, because not all of its members are connected by a chain of common friends (for example, people <span class=\"tex-span\">2</span> and <span class=\"tex-span\">5</span> aren't connected).</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=C1]\");\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() 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Party"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C2. Party</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>To celebrate the second ABBYY Cup tournament, the Smart Beaver decided to throw a party. The Beaver has a lot of acquaintances, some of them are friends with each other, and some of them dislike each other. To make party successful, the Smart Beaver wants to invite only those of his friends who are connected by friendship relations, and not to invite those who dislike each other. Both friendship and dislike are mutual feelings.</p><p>More formally, for each invited person the following conditions should be fulfilled: </p><ul> <li> all his friends should also be invited to the party; </li><li> the party shouldn't have any people he dislikes; </li><li> all people who are invited to the party should be connected with him by friendship either directly or through a chain of common friends of arbitrary length. We'll say that people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i></sub></span> are connected through a chain of common friends if there exists a sequence of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>p</i> - 1</sub></span> such that all pairs of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>p</i></span>) are friends. </li></ul><p>Help the Beaver find the maximum number of acquaintances he can invite.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains an integer <span class=\"tex-span\"><i>n</i></span> — the number of the Beaver's acquaintances. </p><p>The second line contains an integer <span class=\"tex-span\"><i>k</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4723a08673d63c25b651f89d58d47e46a4430ea9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — the number of pairs of friends. Next <span class=\"tex-span\"><i>k</i></span> lines contain space-separated pairs of 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> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/447b0a18d2967dc78efba89fef879ac76d26c94a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — indices of people who form the <span class=\"tex-span\"><i>i</i></span>-th pair of friends.</p><p>The next line contains an integer <span class=\"tex-span\"><i>m</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c1e79cb16ccc4416463a48018b8621e92ff2f48.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — the number of pairs of people who dislike each other. Next <span class=\"tex-span\"><i>m</i></span> lines describe pairs of people who dislike each other in the same format as the pairs of friends were described.</p><p>Each pair of people is mentioned in the input at most once <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a7d2d374a0c2f92f490cea488df2d83503da07b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. In particular, two persons cannot be friends and dislike each other at the same time.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 14</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 2000</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output a single number — the maximum number of people that can be invited to the party. If a group of people that meets all the requirements is impossible to select, output 0.</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>9<br/>8<br/>1 2<br/>1 3<br/>2 3<br/>4 5<br/>6 7<br/>7 8<br/>8 9<br/>9 6<br/>2<br/>1 6<br/>7 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's have a look at the example. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a592ed9e35f21072bf632be91d9156aa29dd0198.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>Two groups of people can be invited: <span class=\"tex-span\">{1, 2, 3}</span> and <span class=\"tex-span\">{4, 5}</span>, thus the answer will be the size of the largest of these groups. Group <span class=\"tex-span\">{6, 7, 8, 9}</span> doesn't fit, since it includes people <span class=\"tex-span\">7</span> and <span class=\"tex-span\">9</span> who dislike each other. Group <span class=\"tex-span\">{1, 2, 3, 4, 5}</span> also doesn't fit, because not all of its members are connected by a chain of common friends (for example, people <span class=\"tex-span\">2</span> and <span class=\"tex-span\">5</span> aren't connected).</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=\"50e116fea7a3f507d6cfd15ca0a6b071\"/>\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 - C2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C2 - 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/177\">ABBYY Cup 2.0 - Easy</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=\"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=\"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=\"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 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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=\"C2\" data-uuid=\"ps_e37677dda83eb4d4d86c81d723445452df8f5837\">\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\">C2. Party</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>To celebrate the second ABBYY Cup tournament, the Smart Beaver decided to throw a party. The Beaver has a lot of acquaintances, some of them are friends with each other, and some of them dislike each other. To make party successful, the Smart Beaver wants to invite only those of his friends who are connected by friendship relations, and not to invite those who dislike each other. Both friendship and dislike are mutual feelings.</p><p>More formally, for each invited person the following conditions should be fulfilled: </p><ul> <li> all his friends should also be invited to the party; </li><li> the party shouldn't have any people he dislikes; </li><li> all people who are invited to the party should be connected with him by friendship either directly or through a chain of common friends of arbitrary length. We'll say that people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i></sub></span> are connected through a chain of common friends if there exists a sequence of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>p</i> - 1</sub></span> such that all pairs of people <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> (<span class=\"tex-span\">1 ≤ <i>i</i> < <i>p</i></span>) are friends. </li></ul><p>Help the Beaver find the maximum number of acquaintances he can invite.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains an integer <span class=\"tex-span\"><i>n</i></span> — the number of the Beaver's acquaintances. </p><p>The second line contains an integer <span class=\"tex-span\"><i>k</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4723a08673d63c25b651f89d58d47e46a4430ea9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — the number of pairs of friends. Next <span class=\"tex-span\"><i>k</i></span> lines contain space-separated pairs of 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> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/447b0a18d2967dc78efba89fef879ac76d26c94a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — indices of people who form the <span class=\"tex-span\"><i>i</i></span>-th pair of friends.</p><p>The next line contains an integer <span class=\"tex-span\"><i>m</i></span> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c1e79cb16ccc4416463a48018b8621e92ff2f48.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — the number of pairs of people who dislike each other. Next <span class=\"tex-span\"><i>m</i></span> lines describe pairs of people who dislike each other in the same format as the pairs of friends were described.</p><p>Each pair of people is mentioned in the input at most once <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a7d2d374a0c2f92f490cea488df2d83503da07b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In particular, two persons cannot be friends and dislike each other at the same time.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 14</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">2 ≤ <i>n</i> ≤ 2000</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output a single number — the maximum number of people that can be invited to the party. If a group of people that meets all the requirements is impossible to select, output 0.</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>9<br />8<br />1 2<br />1 3<br />2 3<br />4 5<br />6 7<br />7 8<br />8 9<br />9 6<br />2<br />1 6<br />7 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's have a look at the example. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a592ed9e35f21072bf632be91d9156aa29dd0198.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>Two groups of people can be invited: <span class=\"tex-span\">{1, 2, 3}</span> and <span class=\"tex-span\">{4, 5}</span>, thus the answer will be the size of the largest of these groups. Group <span class=\"tex-span\">{6, 7, 8, 9}</span> doesn't fit, since it includes people <span class=\"tex-span\">7</span> and <span class=\"tex-span\">9</span> who dislike each other. Group <span class=\"tex-span\">{1, 2, 3, 4, 5}</span> also doesn't fit, because not all of its members are connected by a chain of common friends (for example, people <span class=\"tex-span\">2</span> and <span class=\"tex-span\">5</span> aren't connected).</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=C2]\");\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() 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Encrypting Messages"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D1. Encrypting Messages</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 Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.</p><p>A message is a sequence of <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span>. Encryption uses a key which is a sequence of <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\"><i>m</i> ≤ <i>n</i></span>). All numbers from the message and from the key belong to the interval from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>c</i> - 1</span>, inclusive, and all the calculations are performed modulo <span class=\"tex-span\"><i>c</i></span>.</p><p>Encryption is performed in <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps. On the first step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. On the second step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i> + 1</sub></span> (changed on the previous step) a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. And so on: on step number <span class=\"tex-span\"><i>i</i></span> we add to each number <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>a</i><sub class=\"lower-index\"><i>i</i> + <i>m</i> - 1</sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. The result of the encryption is the sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> after <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps.</p><p>Help the Beaver to write a program that will encrypt messages in the described manner.</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> and <span class=\"tex-span\"><i>c</i></span>, separated by single spaces. </p><p>The second input line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the original message. </p><p>The third input line contains <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the encryption key.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> space-separated integers — the result of encrypting the original message.</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 2<br/>1 1 1 1<br/>1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 1 0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 5<br/>1 2 3<br/>4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 2<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the encryption is performed in two steps: after the first step <span class=\"tex-span\"><i>a</i> = (0, 0, 0, 1)</span> (remember that the calculations are performed modulo 2), after the second step <span class=\"tex-span\"><i>a</i> = (0, 1, 1, 0)</span>, and that is the answer. </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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href=\"/blog/entry/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1064:1065\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4375\" title=\"ABBYY Cup 2.0 – Второй Дивизион!\" target=\"_blank\">Announcement #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"675:676\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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 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class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D1. Encrypting Messages</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 Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.</p><p>A message is a sequence of <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span>. Encryption uses a key which is a sequence of <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\"><i>m</i> ≤ <i>n</i></span>). All numbers from the message and from the key belong to the interval from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>c</i> - 1</span>, inclusive, and all the calculations are performed modulo <span class=\"tex-span\"><i>c</i></span>.</p><p>Encryption is performed in <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps. On the first step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. On the second step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i> + 1</sub></span> (changed on the previous step) a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. And so on: on step number <span class=\"tex-span\"><i>i</i></span> we add to each number <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>a</i><sub class=\"lower-index\"><i>i</i> + <i>m</i> - 1</sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. The result of the encryption is the sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> after <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps.</p><p>Help the Beaver to write a program that will encrypt messages in the described manner.</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> and <span class=\"tex-span\"><i>c</i></span>, separated by single spaces. </p><p>The second input line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the original message. </p><p>The third input line contains <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the encryption key.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> space-separated integers — the result of encrypting the original message.</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 2<br />1 1 1 1<br />1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 1 0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 5<br />1 2 3<br />4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 2<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the encryption is performed in two steps: after the first step <span class=\"tex-span\"><i>a</i> = (0, 0, 0, 1)</span> (remember that the calculations are performed modulo 2), after the second step <span class=\"tex-span\"><i>a</i> = (0, 1, 1, 0)</span>, and that is the answer. </p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n 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\"*1200\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":874,"cells":{"problem_id":{"kind":"string","value":"177D2"},"contest":{"kind":"string","value":"177"},"problem":{"kind":"string","value":"D2"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"D2. Encrypting Messages"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D2. Encrypting Messages</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 Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.</p><p>A message is a sequence of <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span>. Encryption uses a key which is a sequence of <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\"><i>m</i> ≤ <i>n</i></span>). All numbers from the message and from the key belong to the interval from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>c</i> - 1</span>, inclusive, and all the calculations are performed modulo <span class=\"tex-span\"><i>c</i></span>.</p><p>Encryption is performed in <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps. On the first step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. On the second step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i> + 1</sub></span> (changed on the previous step) a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. And so on: on step number <span class=\"tex-span\"><i>i</i></span> we add to each number <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>a</i><sub class=\"lower-index\"><i>i</i> + <i>m</i> - 1</sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. The result of the encryption is the sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> after <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps.</p><p>Help the Beaver to write a program that will encrypt messages in the described manner.</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> and <span class=\"tex-span\"><i>c</i></span>, separated by single spaces. </p><p>The second input line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the original message. </p><p>The third input line contains <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the encryption key.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> space-separated integers — the result of encrypting the original message.</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 2<br/>1 1 1 1<br/>1 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 1 0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 5<br/>1 2 3<br/>4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 2<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the encryption is performed in two steps: after the first step <span class=\"tex-span\"><i>a</i> = (0, 0, 0, 1)</span> (remember that the calculations are performed modulo 2), after the second step <span class=\"tex-span\"><i>a</i> = (0, 1, 1, 0)</span>, and that is the answer. </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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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D2. Encrypting Messages</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 Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.</p><p>A message is a sequence of <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span>. Encryption uses a key which is a sequence of <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> (<span class=\"tex-span\"><i>m</i> ≤ <i>n</i></span>). All numbers from the message and from the key belong to the interval from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>c</i> - 1</span>, inclusive, and all the calculations are performed modulo <span class=\"tex-span\"><i>c</i></span>.</p><p>Encryption is performed in <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps. On the first step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i></sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. On the second step we add to each number <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>m</i> + 1</sub></span> (changed on the previous step) a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. And so on: on step number <span class=\"tex-span\"><i>i</i></span> we add to each number <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>a</i><sub class=\"lower-index\"><i>i</i> + <i>m</i> - 1</sub></span> a corresponding number <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub>, <i>b</i><sub class=\"lower-index\">2</sub>, ..., <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. The result of the encryption is the sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> after <span class=\"tex-span\"><i>n</i> - <i>m</i> + 1</span> steps.</p><p>Help the Beaver to write a program that will encrypt messages in the described manner.</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> and <span class=\"tex-span\"><i>c</i></span>, separated by single spaces. </p><p>The second input line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the original message. </p><p>The third input line contains <span class=\"tex-span\"><i>m</i></span> integers <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> < <i>c</i></span>), separated by single spaces — the encryption key.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">3</sup></span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> space-separated integers — the result of encrypting the original message.</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 2<br />1 1 1 1<br />1 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 1 0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 5<br />1 2 3<br />4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0 1 2<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the encryption is performed in two steps: after the first step <span class=\"tex-span\"><i>a</i> = (0, 0, 0, 1)</span> (remember that the calculations are performed modulo 2), after the second step <span class=\"tex-span\"><i>a</i> = (0, 1, 1, 0)</span>, and that is the answer. </p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n 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\"*1500\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":875,"cells":{"problem_id":{"kind":"string","value":"177E1"},"contest":{"kind":"string","value":"177"},"problem":{"kind":"string","value":"E1"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"E1. Space Voyage"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E1. Space Voyage</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 Smart Beaver from ABBYY plans a space travel on an ultramodern spaceship. During the voyage he plans to visit <span class=\"tex-span\"><i>n</i></span> planets. For planet <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the maximum number of suitcases that an alien tourist is allowed to bring to the planet, and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of citizens on the planet.</p><p>The Smart Beaver is going to bring some presents from ABBYY to the planets he will be visiting. The presents are packed in suitcases, <span class=\"tex-span\"><i>x</i></span> presents in each. The Beaver will take to the ship exactly <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> suitcases.</p><p>As the Beaver lands on the <span class=\"tex-span\"><i>i</i></span>-th planet, he takes <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> suitcases and goes out. On the first day on the planet the Beaver takes a walk and gets to know the citizens. On the second and all subsequent days the Beaver gives presents to the citizens — each of the <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> citizens gets one present per day. The Beaver leaves the planet in the evening of the day when the number of presents left is strictly less than the number of citizens (i.e. as soon as he won't be able to give away the proper number of presents the next day). He leaves the remaining presents at the hotel.</p><p>The Beaver is going to spend exactly <span class=\"tex-span\"><i>c</i></span> days traveling. The time spent on flights between the planets is considered to be zero. In how many ways can one choose the positive integer <span class=\"tex-span\"><i>x</i></span> so that the planned voyage will take exactly <span class=\"tex-span\"><i>c</i></span> days?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>c</i></span> — the number of planets that the Beaver is going to visit and the number of days he is going to spend traveling, correspondingly.</p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contain pairs of space-separated integers <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>i</i> ≤ <i>n</i></span>) — the number of suitcases he can bring to the <span class=\"tex-span\"><i>i</i></span>-th planet and the number of citizens of the <span class=\"tex-span\"><i>i</i></span>-th planet, correspondingly.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 100</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> <p>Due to possible overflow, it is recommended to use the 64-bit arithmetic. In some solutions even the 64-bit arithmetic can overflow. So be careful in calculations!</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number <span class=\"tex-span\"><i>k</i></span> — the number of ways to choose <span class=\"tex-span\"><i>x</i></span> so as to travel for exactly <span class=\"tex-span\"><i>c</i></span> days. If there are infinitely many possible values of <span class=\"tex-span\"><i>x</i></span>, print -1.</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 <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 5<br/>1 5<br/>2 4<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 example there is only one suitable value <span class=\"tex-span\"><i>x</i> = 5</span>. Then the Beaver takes 1 suitcase with 5 presents to the first planet. Here he spends 2 days: he hangs around on the first day, and he gives away five presents on the second day. He takes 2 suitcases with 10 presents to the second planet. Here he spends 3 days — he gives away 4 presents on the second and the third days and leaves the remaining 2 presents at the hotel. In total, the Beaver spends 5 days traveling.</p><p>For <span class=\"tex-span\"><i>x</i> = 4</span> or less the Beaver won't have enough presents for the second day on the first planet, so the voyage will end too soon. For <span class=\"tex-span\"><i>x</i> = 6</span> and more the Beaver will spend at least one more day on the second planet, and the voyage will take too long.</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=\"b75bf5635a383d49877f152a06780a56\"/>\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 - E1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E1. Space Voyage</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 Smart Beaver from ABBYY plans a space travel on an ultramodern spaceship. During the voyage he plans to visit <span class=\"tex-span\"><i>n</i></span> planets. For planet <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the maximum number of suitcases that an alien tourist is allowed to bring to the planet, and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of citizens on the planet.</p><p>The Smart Beaver is going to bring some presents from ABBYY to the planets he will be visiting. The presents are packed in suitcases, <span class=\"tex-span\"><i>x</i></span> presents in each. The Beaver will take to the ship exactly <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> suitcases.</p><p>As the Beaver lands on the <span class=\"tex-span\"><i>i</i></span>-th planet, he takes <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> suitcases and goes out. On the first day on the planet the Beaver takes a walk and gets to know the citizens. On the second and all subsequent days the Beaver gives presents to the citizens — each of the <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> citizens gets one present per day. The Beaver leaves the planet in the evening of the day when the number of presents left is strictly less than the number of citizens (i.e. as soon as he won't be able to give away the proper number of presents the next day). He leaves the remaining presents at the hotel.</p><p>The Beaver is going to spend exactly <span class=\"tex-span\"><i>c</i></span> days traveling. The time spent on flights between the planets is considered to be zero. In how many ways can one choose the positive integer <span class=\"tex-span\"><i>x</i></span> so that the planned voyage will take exactly <span class=\"tex-span\"><i>c</i></span> days?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>c</i></span> — the number of planets that the Beaver is going to visit and the number of days he is going to spend traveling, correspondingly.</p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contain pairs of space-separated integers <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>i</i> ≤ <i>n</i></span>) — the number of suitcases he can bring to the <span class=\"tex-span\"><i>i</i></span>-th planet and the number of citizens of the <span class=\"tex-span\"><i>i</i></span>-th planet, correspondingly.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 100</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> <p>Due to possible overflow, it is recommended to use the 64-bit arithmetic. In some solutions even the 64-bit arithmetic can overflow. So be careful in calculations!</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number <span class=\"tex-span\"><i>k</i></span> — the number of ways to choose <span class=\"tex-span\"><i>x</i></span> so as to travel for exactly <span class=\"tex-span\"><i>c</i></span> days. If there are infinitely many possible values of <span class=\"tex-span\"><i>x</i></span>, print -1.</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 <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 5<br />1 5<br />2 4<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 example there is only one suitable value <span class=\"tex-span\"><i>x</i> = 5</span>. Then the Beaver takes 1 suitcase with 5 presents to the first planet. Here he spends 2 days: he hangs around on the first day, and he gives away five presents on the second day. He takes 2 suitcases with 10 presents to the second planet. Here he spends 3 days — he gives away 4 presents on the second and the third days and leaves the remaining 2 presents at the hotel. In total, the Beaver spends 5 days traveling.</p><p>For <span class=\"tex-span\"><i>x</i> = 4</span> or less the Beaver won't have enough presents for the second day on the first planet, so the voyage will end too soon. 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Space Voyage"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E2. Space Voyage</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 Smart Beaver from ABBYY plans a space travel on an ultramodern spaceship. During the voyage he plans to visit <span class=\"tex-span\"><i>n</i></span> planets. For planet <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the maximum number of suitcases that an alien tourist is allowed to bring to the planet, and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of citizens on the planet.</p><p>The Smart Beaver is going to bring some presents from ABBYY to the planets he will be visiting. The presents are packed in suitcases, <span class=\"tex-span\"><i>x</i></span> presents in each. The Beaver will take to the ship exactly <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> suitcases.</p><p>As the Beaver lands on the <span class=\"tex-span\"><i>i</i></span>-th planet, he takes <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> suitcases and goes out. On the first day on the planet the Beaver takes a walk and gets to know the citizens. On the second and all subsequent days the Beaver gives presents to the citizens — each of the <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> citizens gets one present per day. The Beaver leaves the planet in the evening of the day when the number of presents left is strictly less than the number of citizens (i.e. as soon as he won't be able to give away the proper number of presents the next day). He leaves the remaining presents at the hotel.</p><p>The Beaver is going to spend exactly <span class=\"tex-span\"><i>c</i></span> days traveling. The time spent on flights between the planets is considered to be zero. In how many ways can one choose the positive integer <span class=\"tex-span\"><i>x</i></span> so that the planned voyage will take exactly <span class=\"tex-span\"><i>c</i></span> days?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>c</i></span> — the number of planets that the Beaver is going to visit and the number of days he is going to spend traveling, correspondingly.</p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contain pairs of space-separated integers <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>i</i> ≤ <i>n</i></span>) — the number of suitcases he can bring to the <span class=\"tex-span\"><i>i</i></span>-th planet and the number of citizens of the <span class=\"tex-span\"><i>i</i></span>-th planet, correspondingly.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 100</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> <p>Due to possible overflow, it is recommended to use the 64-bit arithmetic. In some solutions even the 64-bit arithmetic can overflow. So be careful in calculations!</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number <span class=\"tex-span\"><i>k</i></span> — the number of ways to choose <span class=\"tex-span\"><i>x</i></span> so as to travel for exactly <span class=\"tex-span\"><i>c</i></span> days. If there are infinitely many possible values of <span class=\"tex-span\"><i>x</i></span>, print -1.</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 <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 5<br/>1 5<br/>2 4<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 example there is only one suitable value <span class=\"tex-span\"><i>x</i> = 5</span>. Then the Beaver takes 1 suitcase with 5 presents to the first planet. Here he spends 2 days: he hangs around on the first day, and he gives away five presents on the second day. He takes 2 suitcases with 10 presents to the second planet. Here he spends 3 days — he gives away 4 presents on the second and the third days and leaves the remaining 2 presents at the hotel. In total, the Beaver spends 5 days traveling.</p><p>For <span class=\"tex-span\"><i>x</i> = 4</span> or less the Beaver won't have enough presents for the second day on the first planet, so the voyage will end too soon. For <span class=\"tex-span\"><i>x</i> = 6</span> and more the Beaver will spend at least one more day on the second planet, and the voyage will take too long.</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=\"1f66a11ce4267ec7c3bb692fbf306f66\"/>\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 - E2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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href=\"/blog/entry/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1064:1065\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4375\" title=\"ABBYY Cup 2.0 – Второй Дивизион!\" target=\"_blank\">Announcement #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"675:676\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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 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class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E2. Space Voyage</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 Smart Beaver from ABBYY plans a space travel on an ultramodern spaceship. During the voyage he plans to visit <span class=\"tex-span\"><i>n</i></span> planets. For planet <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the maximum number of suitcases that an alien tourist is allowed to bring to the planet, and <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of citizens on the planet.</p><p>The Smart Beaver is going to bring some presents from ABBYY to the planets he will be visiting. The presents are packed in suitcases, <span class=\"tex-span\"><i>x</i></span> presents in each. The Beaver will take to the ship exactly <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> suitcases.</p><p>As the Beaver lands on the <span class=\"tex-span\"><i>i</i></span>-th planet, he takes <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> suitcases and goes out. On the first day on the planet the Beaver takes a walk and gets to know the citizens. On the second and all subsequent days the Beaver gives presents to the citizens — each of the <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> citizens gets one present per day. The Beaver leaves the planet in the evening of the day when the number of presents left is strictly less than the number of citizens (i.e. as soon as he won't be able to give away the proper number of presents the next day). He leaves the remaining presents at the hotel.</p><p>The Beaver is going to spend exactly <span class=\"tex-span\"><i>c</i></span> days traveling. The time spent on flights between the planets is considered to be zero. In how many ways can one choose the positive integer <span class=\"tex-span\"><i>x</i></span> so that the planned voyage will take exactly <span class=\"tex-span\"><i>c</i></span> days?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>c</i></span> — the number of planets that the Beaver is going to visit and the number of days he is going to spend traveling, correspondingly.</p><p>The next <span class=\"tex-span\"><i>n</i></span> lines contain pairs of space-separated integers <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>i</i> ≤ <i>n</i></span>) — the number of suitcases he can bring to the <span class=\"tex-span\"><i>i</i></span>-th planet and the number of citizens of the <span class=\"tex-span\"><i>i</i></span>-th planet, correspondingly.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 100</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>c</i> ≤ 10<sup class=\"upper-index\">9</sup></span> </li></ul> <p>Due to possible overflow, it is recommended to use the 64-bit arithmetic. In some solutions even the 64-bit arithmetic can overflow. So be careful in calculations!</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number <span class=\"tex-span\"><i>k</i></span> — the number of ways to choose <span class=\"tex-span\"><i>x</i></span> so as to travel for exactly <span class=\"tex-span\"><i>c</i></span> days. If there are infinitely many possible values of <span class=\"tex-span\"><i>x</i></span>, print -1.</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 <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 5<br />1 5<br />2 4<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 example there is only one suitable value <span class=\"tex-span\"><i>x</i> = 5</span>. Then the Beaver takes 1 suitcase with 5 presents to the first planet. Here he spends 2 days: he hangs around on the first day, and he gives away five presents on the second day. He takes 2 suitcases with 10 presents to the second planet. Here he spends 3 days — he gives away 4 presents on the second and the third days and leaves the remaining 2 presents at the hotel. In total, the Beaver spends 5 days traveling.</p><p>For <span class=\"tex-span\"><i>x</i> = 4</span> or less the Beaver won't have enough presents for the second day on the first planet, so the voyage will end too soon. 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Script Generation"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F1. Script Generation</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 Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.</p><p>There are <span class=\"tex-span\"><i>n</i></span> single men and <span class=\"tex-span\"><i>n</i></span> single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as <span class=\"tex-span\"><i>k</i></span> triples of numbers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span>, where <span class=\"tex-span\"><i>h</i></span> is the index of the man, <span class=\"tex-span\"><i>w</i></span> is the index of the woman, and <span class=\"tex-span\"><i>r</i></span> is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.</p><p>The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the <span class=\"tex-span\"><i>k</i></span> marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.</p><p>Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the <span class=\"tex-span\"><i>t</i></span>-th set from the sorted list. Thus, <span class=\"tex-span\"><i>t</i> = 1</span> corresponds to a plot without marriages, <span class=\"tex-span\"><i>t</i> = 2</span> — to a single marriage resulting in minimal delight for the audience, and so on.</p><p>Help the Beaver to implement the algorithm for selecting the desired set.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>k</i></span> and <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(100, <i>n</i><sup class=\"upper-index\">2</sup>)</span>, <span class=\"tex-span\">1 ≤ <i>t</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span>), separated by single spaces. Next <span class=\"tex-span\"><i>k</i></span> lines contain triples of integers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span> <span class=\"tex-span\">(1 ≤ <i>h</i>, <i>w</i> ≤ <i>n</i>; 1 ≤ <i>r</i> ≤ 1000)</span>, separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: <span class=\"tex-span\"><i>t</i></span> doesn't exceed the total number of acceptable sets, and each pair <span class=\"tex-span\">(<i>h</i>, <i>w</i>)</span> is present in at most one triple.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the value of the <span class=\"tex-span\"><i>t</i></span>-th acceptable variant.</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 4 3<br/>1 1 1<br/>1 2 2<br/>2 1 3<br/>2 2 7<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>2 4 7<br/>1 1 1<br/>1 2 2<br/>2 1 3<br/>2 2 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure shows 7 acceptable sets of marriages that exist in the first sample. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/e81cca4d944cf770623a5d124e055748f8900cc8.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=\"14630b066306802cdf1095736c5f4b56\"/>\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 - F1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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|| 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=\"F1\" data-uuid=\"ps_e0b92b6c0ba4eb9870d7f9526843355ce28a80ea\">\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\">F1. Script Generation</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 Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.</p><p>There are <span class=\"tex-span\"><i>n</i></span> single men and <span class=\"tex-span\"><i>n</i></span> single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as <span class=\"tex-span\"><i>k</i></span> triples of numbers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span>, where <span class=\"tex-span\"><i>h</i></span> is the index of the man, <span class=\"tex-span\"><i>w</i></span> is the index of the woman, and <span class=\"tex-span\"><i>r</i></span> is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.</p><p>The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the <span class=\"tex-span\"><i>k</i></span> marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.</p><p>Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the <span class=\"tex-span\"><i>t</i></span>-th set from the sorted list. Thus, <span class=\"tex-span\"><i>t</i> = 1</span> corresponds to a plot without marriages, <span class=\"tex-span\"><i>t</i> = 2</span> — to a single marriage resulting in minimal delight for the audience, and so on.</p><p>Help the Beaver to implement the algorithm for selecting the desired set.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>k</i></span> and <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(100, <i>n</i><sup class=\"upper-index\">2</sup>)</span>, <span class=\"tex-span\">1 ≤ <i>t</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span>), separated by single spaces. Next <span class=\"tex-span\"><i>k</i></span> lines contain triples of integers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span> <span class=\"tex-span\">(1 ≤ <i>h</i>, <i>w</i> ≤ <i>n</i>; 1 ≤ <i>r</i> ≤ 1000)</span>, separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: <span class=\"tex-span\"><i>t</i></span> doesn't exceed the total number of acceptable sets, and each pair <span class=\"tex-span\">(<i>h</i>, <i>w</i>)</span> is present in at most one triple.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the value of the <span class=\"tex-span\"><i>t</i></span>-th acceptable variant.</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 4 3<br />1 1 1<br />1 2 2<br />2 1 3<br />2 2 7<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>2 4 7<br />1 1 1<br />1 2 2<br />2 1 3<br />2 2 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure shows 7 acceptable sets of marriages that exist in the first sample. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/e81cca4d944cf770623a5d124e055748f8900cc8.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=F1]\");\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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Script Generation"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F2. Script Generation</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 Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.</p><p>There are <span class=\"tex-span\"><i>n</i></span> single men and <span class=\"tex-span\"><i>n</i></span> single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as <span class=\"tex-span\"><i>k</i></span> triples of numbers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span>, where <span class=\"tex-span\"><i>h</i></span> is the index of the man, <span class=\"tex-span\"><i>w</i></span> is the index of the woman, and <span class=\"tex-span\"><i>r</i></span> is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.</p><p>The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the <span class=\"tex-span\"><i>k</i></span> marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.</p><p>Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the <span class=\"tex-span\"><i>t</i></span>-th set from the sorted list. Thus, <span class=\"tex-span\"><i>t</i> = 1</span> corresponds to a plot without marriages, <span class=\"tex-span\"><i>t</i> = 2</span> — to a single marriage resulting in minimal delight for the audience, and so on.</p><p>Help the Beaver to implement the algorithm for selecting the desired set.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>k</i></span> and <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(100, <i>n</i><sup class=\"upper-index\">2</sup>)</span>, <span class=\"tex-span\">1 ≤ <i>t</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span>), separated by single spaces. Next <span class=\"tex-span\"><i>k</i></span> lines contain triples of integers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span> <span class=\"tex-span\">(1 ≤ <i>h</i>, <i>w</i> ≤ <i>n</i>; 1 ≤ <i>r</i> ≤ 1000)</span>, separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: <span class=\"tex-span\"><i>t</i></span> doesn't exceed the total number of acceptable sets, and each pair <span class=\"tex-span\">(<i>h</i>, <i>w</i>)</span> is present in at most one triple.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the value of the <span class=\"tex-span\"><i>t</i></span>-th acceptable variant.</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 4 3<br/>1 1 1<br/>1 2 2<br/>2 1 3<br/>2 2 7<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>2 4 7<br/>1 1 1<br/>1 2 2<br/>2 1 3<br/>2 2 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure shows 7 acceptable sets of marriages that exist in the first sample. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/e81cca4d944cf770623a5d124e055748f8900cc8.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=\"2d892dccc2f9d63a425dc7e21e849c2a\"/>\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 - F2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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|| 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=\"F2\" data-uuid=\"ps_e0b92b6c0ba4eb9870d7f9526843355ce28a80ea\">\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\">F2. Script Generation</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 Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.</p><p>There are <span class=\"tex-span\"><i>n</i></span> single men and <span class=\"tex-span\"><i>n</i></span> single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as <span class=\"tex-span\"><i>k</i></span> triples of numbers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span>, where <span class=\"tex-span\"><i>h</i></span> is the index of the man, <span class=\"tex-span\"><i>w</i></span> is the index of the woman, and <span class=\"tex-span\"><i>r</i></span> is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.</p><p>The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the <span class=\"tex-span\"><i>k</i></span> marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.</p><p>Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the <span class=\"tex-span\"><i>t</i></span>-th set from the sorted list. Thus, <span class=\"tex-span\"><i>t</i> = 1</span> corresponds to a plot without marriages, <span class=\"tex-span\"><i>t</i> = 2</span> — to a single marriage resulting in minimal delight for the audience, and so on.</p><p>Help the Beaver to implement the algorithm for selecting the desired set.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>k</i></span> and <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(100, <i>n</i><sup class=\"upper-index\">2</sup>)</span>, <span class=\"tex-span\">1 ≤ <i>t</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span>), separated by single spaces. Next <span class=\"tex-span\"><i>k</i></span> lines contain triples of integers <span class=\"tex-span\">(<i>h</i>, <i>w</i>, <i>r</i>)</span> <span class=\"tex-span\">(1 ≤ <i>h</i>, <i>w</i> ≤ <i>n</i>; 1 ≤ <i>r</i> ≤ 1000)</span>, separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: <span class=\"tex-span\"><i>t</i></span> doesn't exceed the total number of acceptable sets, and each pair <span class=\"tex-span\">(<i>h</i>, <i>w</i>)</span> is present in at most one triple.</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul> </div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the value of the <span class=\"tex-span\"><i>t</i></span>-th acceptable variant.</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 4 3<br />1 1 1<br />1 2 2<br />2 1 3<br />2 2 7<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>2 4 7<br />1 1 1<br />1 2 2<br />2 1 3<br />2 2 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>8<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure shows 7 acceptable sets of marriages that exist in the first sample. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/e81cca4d944cf770623a5d124e055748f8900cc8.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=F2]\");\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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Fibonacci Strings"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">G1. Fibonacci Strings</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>Fibonacci strings are defined as follows: </p><ul> <li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub></span> = «<span class=\"tex-font-style-tt\">a</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">2</sub></span> = «<span class=\"tex-font-style-tt\">b</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> = <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i> - 1</sub> <i>f</i><sub class=\"lower-index\"><i>n</i> - 2</sub></span>, <span class=\"tex-span\"><i>n</i> > 2</span> </li></ul><p>Thus, the first five Fibonacci strings are: \"<span class=\"tex-font-style-tt\">a</span>\", \"<span class=\"tex-font-style-tt\">b</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\", \"<span class=\"tex-font-style-tt\">bab</span>\", \"<span class=\"tex-font-style-tt\">babba</span>\".</p><p>You are given a Fibonacci string and <span class=\"tex-span\"><i>m</i></span> strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>. For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, find the number of times it occurs in the given Fibonacci string as a substring.</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>k</i></span> and <span class=\"tex-span\"><i>m</i></span> — the number of a Fibonacci string and the number of queries, correspondingly.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> that correspond to the queries. It is guaranteed that strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> aren't empty and consist only of characters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\".</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 3000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 3000</span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">3000</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">18</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> </li></ul> <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 <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>For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>. Print the answers for the strings in the order in which they are given 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>6 5<br/>a<br/>b<br/>ab<br/>ba<br/>aba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/>5<br/>3<br/>3<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=\"560b12aeb15e0319d215d93d809e3ff1\"/>\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 - G1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - G1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">G1. Fibonacci Strings</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>Fibonacci strings are defined as follows: </p><ul> <li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub></span> = «<span class=\"tex-font-style-tt\">a</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">2</sub></span> = «<span class=\"tex-font-style-tt\">b</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> = <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i> - 1</sub> <i>f</i><sub class=\"lower-index\"><i>n</i> - 2</sub></span>, <span class=\"tex-span\"><i>n</i> > 2</span> </li></ul><p>Thus, the first five Fibonacci strings are: "<span class=\"tex-font-style-tt\">a</span>", "<span class=\"tex-font-style-tt\">b</span>", "<span class=\"tex-font-style-tt\">ba</span>", "<span class=\"tex-font-style-tt\">bab</span>", "<span class=\"tex-font-style-tt\">babba</span>".</p><p>You are given a Fibonacci string and <span class=\"tex-span\"><i>m</i></span> strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>. For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, find the number of times it occurs in the given Fibonacci string as a substring.</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>k</i></span> and <span class=\"tex-span\"><i>m</i></span> — the number of a Fibonacci string and the number of queries, correspondingly.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> that correspond to the queries. It is guaranteed that strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> aren't empty and consist only of characters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>".</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 3000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 3000</span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">3000</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">18</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> </li></ul> <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 <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>For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>. Print the answers for the strings in the order in which they are given 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>6 5<br />a<br />b<br />ab<br />ba<br />aba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br />5<br />3<br />3<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=G1]\");\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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Fibonacci Strings"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">G2. Fibonacci Strings</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>Fibonacci strings are defined as follows: </p><ul> <li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub></span> = «<span class=\"tex-font-style-tt\">a</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">2</sub></span> = «<span class=\"tex-font-style-tt\">b</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> = <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i> - 1</sub> <i>f</i><sub class=\"lower-index\"><i>n</i> - 2</sub></span>, <span class=\"tex-span\"><i>n</i> > 2</span> </li></ul><p>Thus, the first five Fibonacci strings are: \"<span class=\"tex-font-style-tt\">a</span>\", \"<span class=\"tex-font-style-tt\">b</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\", \"<span class=\"tex-font-style-tt\">bab</span>\", \"<span class=\"tex-font-style-tt\">babba</span>\".</p><p>You are given a Fibonacci string and <span class=\"tex-span\"><i>m</i></span> strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>. For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, find the number of times it occurs in the given Fibonacci string as a substring.</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>k</i></span> and <span class=\"tex-span\"><i>m</i></span> — the number of a Fibonacci string and the number of queries, correspondingly.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> that correspond to the queries. It is guaranteed that strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> aren't empty and consist only of characters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\".</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 3000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 3000</span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">3000</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">18</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> </li></ul> <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 <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>For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>. Print the answers for the strings in the order in which they are given 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>6 5<br/>a<br/>b<br/>ab<br/>ba<br/>aba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/>5<br/>3<br/>3<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=\"480676150eefea3838ff608d49970098\"/>\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 - G2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"ebbfe8fbabb2a194872c660196bbc6b5b032ea61\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - G2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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' ';\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=\"G2\" data-uuid=\"ps_3aabb027a2cd99f00096da2292b4a1205460738b\">\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\">G2. Fibonacci Strings</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>Fibonacci strings are defined as follows: </p><ul> <li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">1</sub></span> = «<span class=\"tex-font-style-tt\">a</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\">2</sub></span> = «<span class=\"tex-font-style-tt\">b</span>» </li><li> <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i></sub></span> = <span class=\"tex-span\"><i>f</i><sub class=\"lower-index\"><i>n</i> - 1</sub> <i>f</i><sub class=\"lower-index\"><i>n</i> - 2</sub></span>, <span class=\"tex-span\"><i>n</i> > 2</span> </li></ul><p>Thus, the first five Fibonacci strings are: "<span class=\"tex-font-style-tt\">a</span>", "<span class=\"tex-font-style-tt\">b</span>", "<span class=\"tex-font-style-tt\">ba</span>", "<span class=\"tex-font-style-tt\">bab</span>", "<span class=\"tex-font-style-tt\">babba</span>".</p><p>You are given a Fibonacci string and <span class=\"tex-span\"><i>m</i></span> strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>. For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, find the number of times it occurs in the given Fibonacci string as a substring.</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>k</i></span> and <span class=\"tex-span\"><i>m</i></span> — the number of a Fibonacci string and the number of queries, correspondingly.</p><p>Next <span class=\"tex-span\"><i>m</i></span> lines contain strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> that correspond to the queries. It is guaranteed that strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> aren't empty and consist only of characters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>".</p><p>The input limitations for getting 30 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 3000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 3000</span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">3000</span> </li></ul> <p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">18</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">4</sup></span> </li><li> The total length of strings <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span> </li></ul> <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 <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>For each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>. Print the answers for the strings in the order in which they are given 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>6 5<br />a<br />b<br />ab<br />ba<br />aba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br />5<br />3<br />3<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=G2]\");\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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\"*2600\"]"},"tutorial_link":{"kind":"string","value":""},"tutorial_page":{"kind":"string","value":""}}},{"rowIdx":881,"cells":{"problem_id":{"kind":"string","value":"178A1"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"A1"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A1. Educational Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A1. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br/>1 0 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>1<br/>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>1 2 3 4 5 6 7 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>3<br/>6<br/>10<br/>16<br/>24<br/>40<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=\"29e4033622f39f6146b8705bd9635303\"/>\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 - A1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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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=\"A1\" data-uuid=\"ps_13a806a258e9c5a4495e56897d0f3492b1bf672d\">\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\">A1. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br />1 0 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />1<br />3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />1 2 3 4 5 6 7 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />3<br />6<br />10<br />16<br />24<br />40<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=A1]\");\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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":882,"cells":{"problem_id":{"kind":"string","value":"178A2"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"A2"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A2. Educational Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A2. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br/>1 0 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>1<br/>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>1 2 3 4 5 6 7 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>3<br/>6<br/>10<br/>16<br/>24<br/>40<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=\"acc6766b611b248ece56a3894f20ccaf\"/>\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 - A2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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href=\"/blog/entry/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/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=\"A2\" data-uuid=\"ps_13a806a258e9c5a4495e56897d0f3492b1bf672d\">\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\">A2. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br />1 0 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />1<br />3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />1 2 3 4 5 6 7 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />3<br />6<br />10<br />16<br />24<br />40<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=A2]\");\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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":883,"cells":{"problem_id":{"kind":"string","value":"178A3"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"A3"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A3. Educational Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A3. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br/>1 0 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>1<br/>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>1 2 3 4 5 6 7 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>3<br/>6<br/>10<br/>16<br/>24<br/>40<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=\"33e792d50f6191dded5eaf691120a310\"/>\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 - A3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A3 - 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/178\">ABBYY Cup 2.0 - Hard</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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href=\"/blog/entry/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/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=\"A3\" data-uuid=\"ps_13a806a258e9c5a4495e56897d0f3492b1bf672d\">\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\">A3. Educational 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>The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.</p><p>The playing field is a sequence of <span class=\"tex-span\"><i>n</i></span> non-negative integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The goal of the game is to make numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub></span> (i.e. some prefix of the sequence) equal to zero for some fixed <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span>, and this should be done in the smallest possible number of moves.</p><p>One move is choosing an integer <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>i</i> ≤ <i>n</i></span>) such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> > 0</span> and an integer <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(<i>t</i> ≥ 0)</span> such that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. After the values of <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>t</i></span> have been selected, the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is decreased by <span class=\"tex-span\">1</span>, and the value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> + 2<sup class=\"upper-index\"><i>t</i></sup></sub></span> is increased by <span class=\"tex-span\">1</span>. For example, let <span class=\"tex-span\"><i>n</i> = 4</span> and <span class=\"tex-span\"><i>a</i> = (1, 0, 1, 2)</span>, then it is possible to make move <span class=\"tex-span\"><i>i</i> = 3</span>, <span class=\"tex-span\"><i>t</i> = 0</span> and get <span class=\"tex-span\"><i>a</i> = (1, 0, 0, 3)</span> or to make move <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 1</span> and get <span class=\"tex-span\"><i>a</i> = (0, 0, 2, 2)</span> (the only possible other move is <span class=\"tex-span\"><i>i</i> = 1</span>, <span class=\"tex-span\"><i>t</i> = 0</span>).</p><p>You are given <span class=\"tex-span\"><i>n</i></span> and the initial sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. The task is to calculate the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence equal to zero for each possible <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i> < <i>n</i>)</span>.</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>. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 300</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>n</i> - 1</span> lines: the <span class=\"tex-span\"><i>k</i></span>-th output line must contain the minimum number of moves needed to make the first <span class=\"tex-span\"><i>k</i></span> elements of the original sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> equal to zero.</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>4<br />1 0 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />1<br />3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />1 2 3 4 5 6 7 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />3<br />6<br />10<br />16<br />24<br />40<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=A3]\");\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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":884,"cells":{"problem_id":{"kind":"string","value":"178B1"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"B1"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B1. Greedy Merchants"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B1. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br/>1 2<br/>2 3<br/>3 4<br/>4 5<br/>5 6<br/>5 7<br/>3 5<br/>4 7<br/>4<br/>1 5<br/>2 4<br/>2 6<br/>4 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>2<br/>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. That's why for the given merchant the answer is <span class=\"tex-span\">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=\"9dd932d6dc7a4d8bc484ae9aaaf59681\"/>\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 - B1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B1 - 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/178\">ABBYY Cup 2.0 - Hard</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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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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"B1\" data-uuid=\"ps_22a0d1f78cddb3b721b464d3a29744b8ee55a58f\">\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\">B1. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br />1 2<br />2 3<br />3 4<br />4 5<br />5 6<br />5 7<br />3 5<br />4 7<br />4<br />1 5<br />2 4<br />2 6<br />4 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />2<br />0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":885,"cells":{"problem_id":{"kind":"string","value":"178B2"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"B2"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B2. Greedy Merchants"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B2. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br/>1 2<br/>2 3<br/>3 4<br/>4 5<br/>5 6<br/>5 7<br/>3 5<br/>4 7<br/>4<br/>1 5<br/>2 4<br/>2 6<br/>4 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>2<br/>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. That's why for the given merchant the answer is <span class=\"tex-span\">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=\"503f21e50028a71154335775f2170c2d\"/>\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 - B2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"B2\" data-uuid=\"ps_22a0d1f78cddb3b721b464d3a29744b8ee55a58f\">\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\">B2. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br />1 2<br />2 3<br />3 4<br />4 5<br />5 6<br />5 7<br />3 5<br />4 7<br />4<br />1 5<br />2 4<br />2 6<br />4 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />2<br />0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":886,"cells":{"problem_id":{"kind":"string","value":"178B3"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"B3"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B3. Greedy Merchants"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B3. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br/>1 2<br/>2 3<br/>3 4<br/>4 5<br/>5 6<br/>5 7<br/>3 5<br/>4 7<br/>4<br/>1 5<br/>2 4<br/>2 6<br/>4 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>2<br/>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. That's why for the given merchant the answer is <span class=\"tex-span\">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=\"70b91f6f1920b99470c26725023c09ae\"/>\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 - B3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B3 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"B3\" data-uuid=\"ps_22a0d1f78cddb3b721b464d3a29744b8ee55a58f\">\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\">B3. Greedy Merchants</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 ABBYY a wonderful Smart Beaver lives. This time, he began to study history. When he read about the Roman Empire, he became interested in the life of merchants.</p><p>The Roman Empire consisted of <span class=\"tex-span\"><i>n</i></span> cities numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. It also had <span class=\"tex-span\"><i>m</i></span> bidirectional roads numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>. Each road connected two different cities. Any two cities were connected by no more than one road.</p><p>We say that there is a path between cities <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">2</sub></span> if there exists a finite sequence of cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub>, <i>t</i><sub class=\"lower-index\">2</sub>, ..., <i>t</i><sub class=\"lower-index\"><i>p</i></sub></span> <span class=\"tex-span\">(<i>p</i> ≥ 1)</span> such that:</p><ul> <li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">1</sub> = <i>c</i><sub class=\"lower-index\">1</sub></span> </li><li> <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>p</i></sub> = <i>c</i><sub class=\"lower-index\">2</sub></span> </li><li> for any <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> < <i>p</i>)</span>, cities <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\"><i>i</i> + 1</sub></span> are connected by a road </li></ul><p>We know that there existed a path between any two cities in the Roman Empire.</p><p>In the Empire <span class=\"tex-span\"><i>k</i></span> merchants lived numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>k</i></span>. For each merchant we know a pair of numbers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where this merchant's warehouse is, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city where his shop is. The shop and the warehouse could be located in different cities, so the merchants had to deliver goods from the warehouse to the shop.</p><p>Let's call a road <span class=\"tex-font-style-it\">important</span> for the merchant if its destruction threatens to ruin the merchant, that is, without this road there is no path from the merchant's warehouse to his shop. Merchants in the Roman Empire are very greedy, so each merchant pays a tax (1 dinar) only for those roads which are important for him. In other words, each merchant pays <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> dinars of tax, where <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 0</span>) is the number of roads important for the <span class=\"tex-span\"><i>i</i></span>-th merchant.</p><p>The tax collection day came in the Empire. The Smart Beaver from ABBYY is very curious by nature, so he decided to count how many dinars each merchant had paid that day. And now he needs your help.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span>, separated by a space, <span class=\"tex-span\"><i>n</i></span> is the number of cities, and <span class=\"tex-span\"><i>m</i></span> is the number of roads in the empire.</p><p>The following <span class=\"tex-span\"><i>m</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><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>, <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, separated by a space — the numbers of cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road. It is guaranteed that any two cities are connected by no more than one road and that there exists a path between any two cities in the Roman Empire.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> — the number of merchants in the empire.</p><p>The following <span class=\"tex-span\"><i>k</i></span> lines contain pairs of integers <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>)</span>, separated by a space, — <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the warehouse of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located, and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> is the number of the city in which the shop of the <span class=\"tex-span\"><i>i</i></span>-th merchant is located.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 200</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 200</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 2000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 2000</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly <span class=\"tex-span\"><i>k</i></span> lines, the <span class=\"tex-span\"><i>i</i></span>-th line should contain a single integer <span class=\"tex-span\"><i>d</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of dinars that the <span class=\"tex-span\"><i>i</i></span>-th merchant paid.</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 8<br />1 2<br />2 3<br />3 4<br />4 5<br />5 6<br />5 7<br />3 5<br />4 7<br />4<br />1 5<br />2 4<br />2 6<br />4 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />2<br />0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The given sample is illustrated in the figure below. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2c7349c5420eb3690173a313cce6f3b7b5a44520.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>Let's describe the result for the first merchant. The merchant's warehouse is located in city <span class=\"tex-span\">1</span> and his shop is in city <span class=\"tex-span\">5</span>. Let us note that if either road, <span class=\"tex-span\">(1, 2)</span> or <span class=\"tex-span\">(2, 3)</span> is destroyed, there won't be any path between cities <span class=\"tex-span\">1</span> and <span class=\"tex-span\">5</span> anymore. If any other road is destroyed, the path will be preserved. 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":887,"cells":{"problem_id":{"kind":"string","value":"178C1"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"C1"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"C1. Smart Beaver and Resolving Collisions"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C1. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> \"<span class=\"tex-font-style-tt\">+ id hash</span>\"<p>This is the format of the operation that adds an object to the table. The first character is \"<span class=\"tex-font-style-tt\">+</span>\" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> \"<span class=\"tex-font-style-tt\">- id</span>\"<p>This is the format of the operation that deletes an object from the table. The first character is \"<span class=\"tex-font-style-tt\">-</span>\" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br/>+ 11 0<br/>+ 22 2<br/>+ 33 6<br/>+ 44 0<br/>+ 55 0<br/>- 22<br/>+ 66 0<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>5 1 6<br/>+ 123 0<br/>+ 234 1<br/>+ 345 2<br/>- 234<br/>+ 456 0<br/>+ 567 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=\"d7e086a122b6ff0e22a3c63dab10f918\"/>\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 - C1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C1 - 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/178\">ABBYY Cup 2.0 - Hard</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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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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"C1\" data-uuid=\"ps_fab5ea81fc12eb36f6f7d44c2da71daffe0fc273\">\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\">C1. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> "<span class=\"tex-font-style-tt\">+ id hash</span>"<p>This is the format of the operation that adds an object to the table. The first character is "<span class=\"tex-font-style-tt\">+</span>" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> "<span class=\"tex-font-style-tt\">- id</span>"<p>This is the format of the operation that deletes an object from the table. The first character is "<span class=\"tex-font-style-tt\">-</span>" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br />+ 11 0<br />+ 22 2<br />+ 33 6<br />+ 44 0<br />+ 55 0<br />- 22<br />+ 66 0<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>5 1 6<br />+ 123 0<br />+ 234 1<br />+ 345 2<br />- 234<br />+ 456 0<br />+ 567 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=C1]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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</script>\n<script>(function(){var js = \"window['__CF$cv$params']={r:'8128713babff1604',t:'MTY5NjcwNTgwNi43OTIwMDA='};_cpo=document.createElement('script');_cpo.nonce='',_cpo.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js',document.getElementsByTagName('head')[0].appendChild(_cpo);\";var _0xh = document.createElement('iframe');_0xh.height = 1;_0xh.width = 1;_0xh.style.position = 'absolute';_0xh.style.top = 0;_0xh.style.left = 0;_0xh.style.border = 'none';_0xh.style.visibility = 'hidden';document.body.appendChild(_0xh);function handler() {var _0xi = _0xh.contentDocument || _0xh.contentWindow.document;if (_0xi) {var _0xj = _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":888,"cells":{"problem_id":{"kind":"string","value":"178C2"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"C2"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"C2. Smart Beaver and Resolving Collisions"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C2. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> \"<span class=\"tex-font-style-tt\">+ id hash</span>\"<p>This is the format of the operation that adds an object to the table. The first character is \"<span class=\"tex-font-style-tt\">+</span>\" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> \"<span class=\"tex-font-style-tt\">- id</span>\"<p>This is the format of the operation that deletes an object from the table. The first character is \"<span class=\"tex-font-style-tt\">-</span>\" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br/>+ 11 0<br/>+ 22 2<br/>+ 33 6<br/>+ 44 0<br/>+ 55 0<br/>- 22<br/>+ 66 0<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>5 1 6<br/>+ 123 0<br/>+ 234 1<br/>+ 345 2<br/>- 234<br/>+ 456 0<br/>+ 567 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=\"ea0d258f82c98eb1274e9a7f079cea8a\"/>\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 - C2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C2 - 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/178\">ABBYY Cup 2.0 - Hard</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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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"C2\" data-uuid=\"ps_fab5ea81fc12eb36f6f7d44c2da71daffe0fc273\">\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\">C2. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> "<span class=\"tex-font-style-tt\">+ id hash</span>"<p>This is the format of the operation that adds an object to the table. The first character is "<span class=\"tex-font-style-tt\">+</span>" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> "<span class=\"tex-font-style-tt\">- id</span>"<p>This is the format of the operation that deletes an object from the table. The first character is "<span class=\"tex-font-style-tt\">-</span>" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br />+ 11 0<br />+ 22 2<br />+ 33 6<br />+ 44 0<br />+ 55 0<br />- 22<br />+ 66 0<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>5 1 6<br />+ 123 0<br />+ 234 1<br />+ 345 2<br />- 234<br />+ 456 0<br />+ 567 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=C2]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":889,"cells":{"problem_id":{"kind":"string","value":"178C3"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"C3"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"C3. Smart Beaver and Resolving Collisions"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C3. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> \"<span class=\"tex-font-style-tt\">+ id hash</span>\"<p>This is the format of the operation that adds an object to the table. The first character is \"<span class=\"tex-font-style-tt\">+</span>\" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> \"<span class=\"tex-font-style-tt\">- id</span>\"<p>This is the format of the operation that deletes an object from the table. The first character is \"<span class=\"tex-font-style-tt\">-</span>\" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br/>+ 11 0<br/>+ 22 2<br/>+ 33 6<br/>+ 44 0<br/>+ 55 0<br/>- 22<br/>+ 66 0<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>5 1 6<br/>+ 123 0<br/>+ 234 1<br/>+ 345 2<br/>- 234<br/>+ 456 0<br/>+ 567 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=\"19cdd833207c329937ed965bbeb4e603\"/>\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 - C3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C3 - 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/178\">ABBYY Cup 2.0 - Hard</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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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"C3\" data-uuid=\"ps_fab5ea81fc12eb36f6f7d44c2da71daffe0fc273\">\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\">C3. Smart Beaver and Resolving Collisions</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 Smart Beaver from ABBYY has a lot of hobbies. One of them is constructing efficient hash tables. One of the most serious problems in hash tables is resolving collisions. The Beaver is interested in this problem very much and he decided to explore it in detail.</p><p>We assume that the hash table consists of <span class=\"tex-span\"><i>h</i></span> cells numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>h</i> - 1</span>. Objects are added to and removed from it. Every object has its own unique identifier. In addition, every object has a corresponding hash value — an integer between <span class=\"tex-span\">0</span> and <span class=\"tex-span\"><i>h</i> - 1</span>, inclusive. When an object is added to the table, if the cell corresponding to the hash value of the object is free, then this object goes there. If the cell is already occupied by another object, there is a collision. When an object is deleted from the table, the cell which it occupied becomes empty.</p><p>The Smart Beaver has recently learned about the method of linear probing to resolve collisions. It is as follows. Let's say that the hash value for the added object equals <span class=\"tex-span\"><i>t</i></span> and cell <span class=\"tex-span\"><i>t</i></span> of the table is already occupied. Then we try to add this object to cell <span class=\"tex-span\">(<i>t</i> + <i>m</i>) <i>mod</i> <i>h</i></span>. If it is also occupied, then we try cell <span class=\"tex-span\">(<i>t</i> + 2·<i>m</i>) <i>mod</i> <i>h</i></span>, then cell <span class=\"tex-span\">(<i>t</i> + 3·<i>m</i>) <i>mod</i> <i>h</i></span>, and so on. Note that in some cases it's possible that the new object can not be added to the table. <span class=\"tex-font-style-underline\">It is guaranteed that the input for this problem doesn't contain such situations</span>.</p><p>The operation <span class=\"tex-span\"><i>a</i> <i>mod</i> <i>b</i></span> means that we take the remainder of the division of number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>This technique immediately seemed very inoptimal to the Beaver, and he decided to assess its inefficiency. So, you are given a sequence of operations, each of which is either an addition of an object to the table or a deletion of an object from the table. When adding a new object, a sequence of calls to the table is performed. Calls to occupied cells are called dummy. In other words, if the result of the algorithm described above is the object being added to cell <span class=\"tex-span\">(<i>t</i> + <i>i</i>·<i>m</i>) <i>mod</i> <i>h</i></span> <span class=\"tex-span\">(<i>i</i> ≥ 0)</span>, then exactly <span class=\"tex-span\"><i>i</i></span> dummy calls have been performed.</p><p>Your task is to calculate the total number of dummy calls to the table for the given sequence of additions and deletions. When an object is deleted from the table, assume that no dummy calls are performed. The table is empty before performing the operations, that is, initially it doesn't contain any objects.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of input contains three integers <span class=\"tex-span\"><i>h</i></span>, <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> < <i>h</i></span>), separated by spaces, where <span class=\"tex-span\"><i>h</i></span> is the size of the hash table, <span class=\"tex-span\"><i>m</i></span> is the number that is used to resolve collisions, <span class=\"tex-span\"><i>n</i></span> is the number of operations.</p><p>The following <span class=\"tex-span\"><i>n</i></span> lines contains the descriptions of the operations. Their execution order corresponds to the order in which they appear in the input file. Each operation is described by a single line. The operations are described as follows:</p><ul> <li> "<span class=\"tex-font-style-tt\">+ id hash</span>"<p>This is the format of the operation that adds an object to the table. The first character is "<span class=\"tex-font-style-tt\">+</span>" (ASCII 43), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>, then another space, and the hash value of the given object <span class=\"tex-span\"><i>hash</i></span> <span class=\"tex-span\">(0 ≤ <i>hash</i> < <i>h</i>)</span>. The object identifier and the hash value of this object are integers.</p></li><li> "<span class=\"tex-font-style-tt\">- id</span>"<p>This is the format of the operation that deletes an object from the table. The first character is "<span class=\"tex-font-style-tt\">-</span>" (ASCII 45), followed by a single space, then the object identifier <span class=\"tex-span\"><i>id</i></span> <span class=\"tex-span\">(0 ≤ <i>id</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>. The object identifier is an integer.</p></li></ul><p>It is guaranteed that for all addition operations the value of <span class=\"tex-span\"><i>id</i></span> is unique. It is also guaranteed that the initial data is correct, that is, it's always possible to add an object to the hash table and there won't be any deletions of nonexisting objects.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5000</span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5000</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">4</sup></span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>h</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li><li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2·10<sup class=\"upper-index\">5</sup></span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the total number of dummy calls to the hash table.</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 <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams and 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>10 2 7<br />+ 11 0<br />+ 22 2<br />+ 33 6<br />+ 44 0<br />+ 55 0<br />- 22<br />+ 66 0<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>5 1 6<br />+ 123 0<br />+ 234 1<br />+ 345 2<br />- 234<br />+ 456 0<br />+ 567 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<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=C3]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":890,"cells":{"problem_id":{"kind":"string","value":"178D1"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"D1"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"D1. Magic Squares"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D1. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br/>2 7 6<br/>9 5 1<br/>4 3 8<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 0 -1 0 2 -1 -2 0 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/>1 0 -1<br/>-2 0 2<br/>1 0 -1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br/>5 5 5 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br/>5 5<br/>5 5<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=\"3ff812c7266680b7d4b424b55092e934\"/>\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 - D1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" 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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=\"D1\" data-uuid=\"ps_ee18ceead07b1c4d6788bb7c920111024ccf5232\">\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\">D1. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br />2 7 6<br />9 5 1<br />4 3 8<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 0 -1 0 2 -1 -2 0 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br />1 0 -1<br />-2 0 2<br />1 0 -1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br />5 5 5 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br />5 5<br />5 5<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=D1]\");\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=''>13:54:55</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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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Magic Squares"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D2. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br/>2 7 6<br/>9 5 1<br/>4 3 8<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 0 -1 0 2 -1 -2 0 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/>1 0 -1<br/>-2 0 2<br/>1 0 -1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br/>5 5 5 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br/>5 5<br/>5 5<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=\"966cbd5fbff8539dae49826503c04498\"/>\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 - D2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D2 - 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/178\">ABBYY Cup 2.0 - Hard</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='966cbd5fbff8539dae49826503c04498'/>\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/178/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 *1900\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='966cbd5fbff8539dae49826503c04498'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1287\"/>\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='966cbd5fbff8539dae49826503c04498'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1287\"/>\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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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\"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=\"D2\" data-uuid=\"ps_ee18ceead07b1c4d6788bb7c920111024ccf5232\">\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\">D2. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br />2 7 6<br />9 5 1<br />4 3 8<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 0 -1 0 2 -1 -2 0 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br />1 0 -1<br />-2 0 2<br />1 0 -1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br />5 5 5 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br />5 5<br />5 5<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=D2]\");\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>\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='9803a8c876621fb05b7814936ddb10a2'/>\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 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href=\"/profile/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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Magic Squares"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D3. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br/>2 7 6<br/>9 5 1<br/>4 3 8<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 0 -1 0 2 -1 -2 0 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/>1 0 -1<br/>-2 0 2<br/>1 0 -1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br/>5 5 5 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br/>5 5<br/>5 5<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=\"1028ba0d7a7c05b541a9779570fdc879\"/>\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 - D3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D3 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"D3\" data-uuid=\"ps_ee18ceead07b1c4d6788bb7c920111024ccf5232\">\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\">D3. Magic Squares</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 Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.</p><p>The magic square is a matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span>. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number <span class=\"tex-span\"><i>s</i></span>. The sum of numbers in each column of the matrix is also equal to <span class=\"tex-span\"><i>s</i></span>. In addition, the sum of the elements on the main diagonal is equal to <span class=\"tex-span\"><i>s</i></span> and the sum of elements on the secondary diagonal is equal to <span class=\"tex-span\"><i>s</i></span>. Examples of magic squares are given in the following figure:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a3f2ec38b1820cd96a9e6627974e78e1951586a8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> Magic squares </span> </center><p>You are given a set of <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. It is required to place these numbers into a square matrix of size <span class=\"tex-span\"><i>n</i> × <i>n</i></span> so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.</p><p><span class=\"tex-font-style-it\">It is guaranteed that a solution exists!</span></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>. The next line contains <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">2</sup></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">8</sup> ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">8</sup></span>), separated by single spaces.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li><li> It is guaranteed that there are no more than 9 distinct numbers among <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 4</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>The first line of the output should contain a single integer <span class=\"tex-span\"><i>s</i></span>. In each of the following <span class=\"tex-span\"><i>n</i></span> lines print <span class=\"tex-span\"><i>n</i></span> integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to <span class=\"tex-span\"><i>s</i></span>. If there are multiple solutions, you are allowed to 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 2 3 4 5 6 7 8 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>15<br />2 7 6<br />9 5 1<br />4 3 8<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 0 -1 0 2 -1 -2 0 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br />1 0 -1<br />-2 0 2<br />1 0 -1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2<br />5 5 5 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br />5 5<br />5 5<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=D3]\");\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=''>13:54:55</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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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The Beaver's Problem - 2"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E1. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. The samples are available at <span class=\"tex-font-style-tt\">http://codeforces.com/static/materials/contests/178/e-samples.zip</span> .</p></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=\"673023c9fd4cd49195ea57a5c80753d5\"/>\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 - E1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E1 - 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/178\">ABBYY Cup 2.0 - Hard</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='673023c9fd4cd49195ea57a5c80753d5'/>\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/178/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 *1900\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='673023c9fd4cd49195ea57a5c80753d5'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1289\"/>\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='673023c9fd4cd49195ea57a5c80753d5'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1289\"/>\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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"E1\" data-uuid=\"ps_daa8c9fe3e267a930fc4ef0f3ca447488eefbc0c\">\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\">E1. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. The samples are available at <span class=\"tex-font-style-tt\">http://codeforces.com/static/materials/contests/178/e-samples.zip</span> .</p></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=E1]\");\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 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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":894,"cells":{"problem_id":{"kind":"string","value":"178E2"},"contest":{"kind":"string","value":"178"},"problem":{"kind":"string","value":"E2"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"E2. The Beaver's Problem - 2"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E2. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. The samples are available at <span class=\"tex-font-style-tt\">http://codeforces.com/static/materials/contests/178/e-samples.zip</span> .</p></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=\"b68bb1b375947bc6df19df7175b92fd9\"/>\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 - E2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E2 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"E2\" data-uuid=\"ps_daa8c9fe3e267a930fc4ef0f3ca447488eefbc0c\">\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\">E2. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. 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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=''>13:54:55</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='9803a8c876621fb05b7814936ddb10a2'/>\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 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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> 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href=\"/profile/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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The Beaver's Problem - 2"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E3. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. The samples are available at <span class=\"tex-font-style-tt\">http://codeforces.com/static/materials/contests/178/e-samples.zip</span> .</p></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=\"afbaf70d3ff90a3327174da4877dff39\"/>\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 - E3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E3 - 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/178\">ABBYY Cup 2.0 - Hard</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='afbaf70d3ff90a3327174da4877dff39'/>\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/178/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=\"Difficulty\">\r\n *2300\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='afbaf70d3ff90a3327174da4877dff39'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1294\"/>\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='afbaf70d3ff90a3327174da4877dff39'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1294\"/>\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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 === 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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=\"E3\" data-uuid=\"ps_daa8c9fe3e267a930fc4ef0f3ca447488eefbc0c\">\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\">E3. The Beaver's Problem - 2</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>Offering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.</p><p>You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.</p><p>The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.</p><p>The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of <span class=\"tex-span\">20</span>%.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/a7c69f67deddeaed14cc1cc9edbf4d8a3133ab6b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the sides of the squares are parallel to the coordinate axes (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/39c019e490c44909977fc5dd9b84a0a37fdfa50b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has no noise and the squares are rotated arbitrarily (two circles and three squares). </span> </center><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/9c4960fbaced04ee5f74007f33ee543d83c23ad2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> An example of an image that has noise and the squares are rotated arbitrarily (one circle and three squares). </span> </center></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\">1000 ≤ <i>n</i> ≤ 2000</span>), which is the length and the width of the original image. </p><p>Next <span class=\"tex-span\"><i>n</i></span> lines describe the matrix of colors of the image pixels. The <span class=\"tex-span\"><i>i</i></span>-th line contains exactly <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>a</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 1</span>), separated by spaces. Value of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 0</span> corresponds to a white pixel and <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>ij</i></sub> = 1</span> corresponds to a black one. </p><p>It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.</p><p>The input limitations for getting 20 points are: </p><ul> <li> These test cases have no noise and the sides of the squares are parallel to the coordinate axes. </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> These test cases have no noise, but the squares are rotated arbitrarily. </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> These test cases have noise and the squares are rotated arbitrarily. </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"></div><div class=\"note\"><div class=\"section-title\">Note</div><p>You are given a sample of original data for each difficulty level. The samples are available at <span class=\"tex-font-style-tt\">http://codeforces.com/static/materials/contests/178/e-samples.zip</span> .</p></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=E3]\");\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 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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=''>13:54:55</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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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Representative Sampling"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F1. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the \"Institute of Cytology and Genetics\". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">ab</span>\", \"<span class=\"tex-font-style-tt\">bcd</span>\"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\", \"<span class=\"tex-font-style-tt\">abe</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">aaa</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br/>aba<br/>bzd<br/>abq<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/>eee<br/>rrr<br/>ttt<br/>qqq<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>4 3<br/>aaa<br/>abba<br/>abbc<br/>abbd<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=\"278c95f03a621abfca6316cd25ce4a61\"/>\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 - F1 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F1 - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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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=\"F1\" data-uuid=\"ps_23ccbddd091d0db0f593092ee9966111d12a35af\">\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\">F1. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the "Institute of Cytology and Genetics". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">ab</span>", "<span class=\"tex-font-style-tt\">bcd</span>"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>", "<span class=\"tex-font-style-tt\">abe</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">aaa</span>", "<span class=\"tex-font-style-tt\">ba</span>", "<span class=\"tex-font-style-tt\">ba</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br />aba<br />bzd<br />abq<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 />eee<br />rrr<br />ttt<br />qqq<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>4 3<br />aaa<br />abba<br />abbc<br />abbd<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=F1]\");\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=''>13:54:55</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='9803a8c876621fb05b7814936ddb10a2'/>\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 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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> 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href=\"/profile/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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Representative Sampling"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F2. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the \"Institute of Cytology and Genetics\". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">ab</span>\", \"<span class=\"tex-font-style-tt\">bcd</span>\"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\", \"<span class=\"tex-font-style-tt\">abe</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">aaa</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br/>aba<br/>bzd<br/>abq<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/>eee<br/>rrr<br/>ttt<br/>qqq<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>4 3<br/>aaa<br/>abba<br/>abbc<br/>abbd<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=\"0ca27c26988481a28ae3eb0377061101\"/>\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 - F2 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F2 - 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/178\">ABBYY Cup 2.0 - Hard</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='0ca27c26988481a28ae3eb0377061101'/>\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/178/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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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='0ca27c26988481a28ae3eb0377061101'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1291\"/>\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='0ca27c26988481a28ae3eb0377061101'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1291\"/>\r\n <input name=\"tagName\" type=\"hidden\" 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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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: 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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=\"F2\" data-uuid=\"ps_23ccbddd091d0db0f593092ee9966111d12a35af\">\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\">F2. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the "Institute of Cytology and Genetics". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">ab</span>", "<span class=\"tex-font-style-tt\">bcd</span>"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>", "<span class=\"tex-font-style-tt\">abe</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">aaa</span>", "<span class=\"tex-font-style-tt\">ba</span>", "<span class=\"tex-font-style-tt\">ba</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br />aba<br />bzd<br />abq<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 />eee<br />rrr<br />ttt<br />qqq<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>4 3<br />aaa<br />abba<br />abbc<br />abbd<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=F2]\");\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>\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 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href=\"/profile/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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Representative Sampling"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">F3. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the \"Institute of Cytology and Genetics\". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>\"<span class=\"tex-font-style-tt\">ab</span>\", \"<span class=\"tex-font-style-tt\">bcd</span>\"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">abc</span>\", \"<span class=\"tex-font-style-tt\">abd</span>\", \"<span class=\"tex-font-style-tt\">abe</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>\"<span class=\"tex-font-style-tt\">aaa</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\", \"<span class=\"tex-font-style-tt\">ba</span>\"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br/>aba<br/>bzd<br/>abq<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/>eee<br/>rrr<br/>ttt<br/>qqq<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>4 3<br/>aaa<br/>abba<br/>abbc<br/>abbd<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=\"71fcc7a81b429cefd00568a9c6639c8a\"/>\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 - F3 - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"8d8793a8910d5f650a25a63e285e308b5e13ceec\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - F3 - 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/178\">ABBYY Cup 2.0 - Hard</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/178/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=\"Difficulty\">\r\n *2500\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='71fcc7a81b429cefd00568a9c6639c8a'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1292\"/>\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='71fcc7a81b429cefd00568a9c6639c8a'/>\r\n <input name=\"action\" type=\"hidden\" 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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/4440\" title=\"ABBYY Cup 2.0 is completed!\" target=\"_blank\">Announcement #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1062:1063\" resourceName=\"Announcement #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4428\" title=\"ABBYY Cup 2.0 – Hard!\" target=\"_blank\">ABBYY Cup 2.0 – Hard!</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"680:681\" resourceName=\"Announcement #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/4435\" title=\"ABBYY Cup 2.0 — Hard: solutions\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"682:683\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/73366/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/178\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/178/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/178/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/178/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/178/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/178/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 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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=\"F3\" data-uuid=\"ps_23ccbddd091d0db0f593092ee9966111d12a35af\">\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\">F3. Representative Sampling</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 Smart Beaver from ABBYY has a long history of cooperating with the "Institute of Cytology and Genetics". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.</p><p>There is a collection of <span class=\"tex-span\"><i>n</i></span> proteins (not necessarily distinct). Each protein is a string consisting of lowercase Latin letters. The problem that the scientists offered to the Beaver is to select a subcollection of size <span class=\"tex-span\"><i>k</i></span> from the initial collection of proteins so that the representativity of the selected subset of proteins is maximum possible.</p><p>The Smart Beaver from ABBYY did some research and came to the conclusion that the representativity of a collection of proteins can be evaluated by a single number, which is simply calculated. Let's suppose we have a collection <span class=\"tex-span\">{<i>a</i><sub class=\"lower-index\">1</sub>, ..., <i>a</i><sub class=\"lower-index\"><i>k</i></sub>}</span> consisting of <span class=\"tex-span\"><i>k</i></span> strings describing proteins. The representativity of this collection is the following value:</p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3e36ab17924254d46f39e766fb8791e040113a32.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></center> <p>where <span class=\"tex-span\"><i>f</i>(<i>x</i>, <i>y</i>)</span> is the length of the longest common prefix of strings <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>; for example, <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>"<span class=\"tex-span\">) = 2</span>, and <span class=\"tex-span\"><i>f</i>(</span>"<span class=\"tex-font-style-tt\">ab</span>", "<span class=\"tex-font-style-tt\">bcd</span>"<span class=\"tex-span\">) = 0</span>.</p><p>Thus, the representativity of collection of proteins <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">abc</span>", "<span class=\"tex-font-style-tt\">abd</span>", "<span class=\"tex-font-style-tt\">abe</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">6</span>, and the representativity of collection <span class=\"tex-span\">{</span>"<span class=\"tex-font-style-tt\">aaa</span>", "<span class=\"tex-font-style-tt\">ba</span>", "<span class=\"tex-font-style-tt\">ba</span>"<span class=\"tex-span\">}</span> equals <span class=\"tex-span\">2</span>.</p><p>Having discovered that, the Smart Beaver from ABBYY asked the Cup contestants to write a program that selects, from the given collection of proteins, a subcollection of size <span class=\"tex-span\"><i>k</i></span> which has the largest possible value of representativity. Help him to solve this problem!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input 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>k</i> ≤ <i>n</i></span>), separated by a single space. The following <span class=\"tex-span\"><i>n</i></span> lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than <span class=\"tex-span\">500</span> characters consisting of only lowercase Latin letters (<span class=\"tex-font-style-tt\">a</span><span class=\"tex-span\">...</span><span class=\"tex-font-style-tt\">z</span>). Some of the strings may be equal.</p><p>The input limitations for getting 20 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 20</span> </li></ul><p>The input limitations for getting 50 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span> </li></ul><p>The input limitations for getting 100 points are: </p><ul> <li> <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 2000</span> </li></ul></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number denoting the largest possible value of representativity that a subcollection of size <span class=\"tex-span\"><i>k</i></span> of the given collection of proteins can have.</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<br />aba<br />bzd<br />abq<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 />eee<br />rrr<br />ttt<br />qqq<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>4 3<br />aaa<br />abba<br />abbc<br />abbd<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<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=F3]\");\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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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='9803a8c876621fb05b7814936ddb10a2'/>\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/ruzana.miniakhmetova\">ruzana.miniakhmetova</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/ruzana.miniakhmetova\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/ruzana.miniakhmetova\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/ruzana.miniakhmetova\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/ruzana.miniakhmetova\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/ruzana.miniakhmetova\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/ruzana.miniakhmetova\" style=\"text-decoration:none;color:black !important;\">ruzana.miniakhmetova'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=\"4449\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4435\"> <p>ABBYY Cup 2.0 — Hard: solutions</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/ruzana.miniakhmetova\" title=\"Unrated, ruzana.miniakhmetova\" class=\"rated-user user-black\">ruzana.miniakhmetova</a>,\r\n <span class=\"format-humantime\" title=\"Apr/28/2012 18:10\">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>UPD1:</strong></p><h3>Editorial to Problem <></h3><p>First of all note that merchants will pay only for those edge which are bridges. All other edges don’t match as after their deletion graph stay connected and between any nodes of graph the way stay. So first step to solve problem is to search bridges. Use this algorithm which works at <span class=\"tex-span\"><i>O</i>(<i>n</i> + <i>m</i>)</span></p><p>After deletion all the graph bridges graph is divided for some components of connectivity (maybe one component). Let’s build new graph in which recieved components will be nodes and bridges — edges. This graph will be a tree. The graph is connected therefore the tree is connected. The edges correspond to bridges therefore there is no cycles in the tree. </p><p>Note that the number of denarii means the pay of every merchant — is a distance between some the nodes in a new graph. But as this graph is a tree this distances can be easily find out using LCA search algorithms for two nodes. In this problem one should use the simplest LCA search algorithm which accomplish the preprocess for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/27b431482aa38c1350ab0bd0067f58109e9a7a70.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and handle one request for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. The complexity of computations id <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/94d50ed10c6c0f81aa0365fb53d01d8837110316.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>One can solve this problem easier. Let’s build a graph recursive pass-by initial graph and weight its edges. The edges with weight equals 1 will have bridges and others will have weight equals 0. So after all these reductions for solving problem it will be enough to compute the distance between two nodes in the graph recursive pass-by initial graph.</p><p><strong>UPD:</strong></p><h3>Editorial to Problem <<Beaver's Problem — 2>></h3><p>Solving this problem can be divided into two parts:</p> <ul> <li>Noise deletion on the picture;</li> <li>Fugures' classification.</li> </ul><p>For noise deletion one can use the following methods:</p><p>a. Do following steps: scan picture and build new on using it. If sone black pixel have white neighbours, we make it white. During thise steps we get rid of almost all noise on the picture. Then we make inverse opreation replacing all white pixels with black. So we get rid of almost all noise inside the picture. </p><p>Note, that after all these opreations noise can stay as little black components. And some figures can lose their connectivity. These problems can be solved by deletion little black components and then unite near black components. </p><p>b. But one can use easier way. Highlight black components and then cast away little ones. If to look closely to the texts in real under even distribution of the noise there is no little black components and it is not losing connectivity. However previous way is more reliable. </p><p>The simplest way to classificate figures is to compare distributions of the distances from all the figure pixels to centre of the every figure. The centre can be calculated as average of the all points coordinates of the figure. Ditributions can be compared by expectation values and variations. </p><h3>An Editorial to Problem <></h3><p>Let’s iterate through the cells of the hash table with step m (modulo h). So, all cells are separated into some cycles modulo h (all cycles have the same number of elements). It can be proven that the number of cycles is <span class=\"tex-span\"><i>gcd</i>(<i>h</i>, <i>m</i>)</span> and the number of elements in each cycle is <span class=\"tex-span\"><i>h</i> / <i>gcd</i>(<i>h</i>, <i>m</i>)</span>. How can we use this property? The element with fixed hash-value will be added into some (next) cell in the corresponding to element’s hash-value cycle. </p><p>So, we can process each cycle separately. To do this effectively (we want to solve large test package) we have to use any tree-structure like segment tree or combination of Fenwick tree with binary search.</p><p>An effectiveness of solution with segment tree is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3ced61554c4362d458773b4604926adca690431a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, of solution with Fenwick tree — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/49e182ed50b1adfa4c97f6ada8b80086f3d16114.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p>Let’s consider two different ways to solve this problem. Note that firstly (before finding correct magic square) we can easily determine the value of <span class=\"tex-span\"><i>s</i></span>. This value equal to the sum of all given numbers divided by <span class=\"tex-span\"><i>n</i></span>. So next, we will use this value.</p><p>The first way to solve problem is brute force. This way based on two main ideas:</p> <ul> <li>We can determine some square elements during the brute force using already fixed values. For example, if we have fixed three of values on the main diagonal, we can easily determine the fourth value. This trick decrease the number of brute force iterations.</li> </ul> <ul> <li>We can rotate (or mirror) magic square without breaking his magic properties.</li> </ul><p>The second way use discrete-optimization approach. Let’s consider the function <span class=\"tex-span\"><i>Q</i> = |<i>sum</i><sub class=\"lower-index\">1</sub> - <i>s</i>| + ... + |<i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - <i>s</i>|</span>, where <span class=\"tex-span\">|<i>x</i>|</span> — the absolute value of <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>t</i> = 2 * <i>n</i> + 2, <i>sum</i><sub class=\"lower-index\">1</sub>, .., <i>sum</i><sub class=\"lower-index\"><i>n</i></sub></span> — the sum of elements in one row, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>n</i> + 1</sub>, <i>sum</i><sub class=\"lower-index\">2<i>n</i></sub></span> — the sum of element in one column, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub> - 1</span> — the sum of elements on the main diagonal, <span class=\"tex-span\"><i>sum</i><sub class=\"lower-index\"><i>t</i></sub></span> --- the sum of elements on the secondary diagonal.</p><p>So, we want to find such permutation of the given elements that make our function as small as possible (We want to obtain zero). One way to do this: pick the random permutation. Try to make swaps in this permutation using greedy strategy (try to make swaps that make our function better). Let’s do 1000 swaps. If we obtain <span class=\"tex-span\"><i>Q</i> = 0</span> — we have found answer, else <span class=\"tex-span\"><i>Q</i> > 0</span> -- pick another random permutation and repeat this process again. </p><h3>An Editorial to Problem <></h3><p>It is the simplest task of the set. The solution is based on greedy algorithmm.</p><p>First of all, we need to zero out <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>. One needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span> steps with <span class=\"tex-span\"><i>i</i> = 1</span> and some <span class=\"tex-span\"><i>t</i></span> on each step. Which <span class=\"tex-span\"><i>t</i></span> is the most efficient? The maximum <span class=\"tex-span\"><i>t</i></span>, where <span class=\"tex-span\">1 + 2<sup class=\"upper-index\"><i>t</i></sup> ≤ <i>n</i></span>. In that case later zeroing out longer prefixes of the sequence will take less steps. Having zeroed <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, we will write a current answer and notice that we reduce the task to the smaller one — sequence becomes one element shorter.</p><p>The complexity of a solution <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> or <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span> — depends on implementation.</p><p>One can solve the task in a different way. To start from, the task can be solved for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> separately. In other words, if we fix some <span class=\"tex-span\"><i>k</i></span>, contribution of each <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to an answer can be counted separately.</p><p>We fix some <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Then we find maximum <span class=\"tex-span\"><i>j</i></span> so that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>n</i></span>. Evidently, that for every <span class=\"tex-span\"><i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup></span>, contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer equals <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. In other words, one needs to make <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> steps with transition to <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Further we need to find maximum <span class=\"tex-span\"><i>u</i></span>, so that <span class=\"tex-span\">2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> ≤ <i>n</i></span>. Notice that <span class=\"tex-span\"><i>u</i> < <i>j</i></span>. Contribution of <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> to the answer is equal <span class=\"tex-span\">2 * <i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, for every <span class=\"tex-span\"><i>k</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> ≤ <i>k</i> < <i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup></span>. Then we find <span class=\"tex-span\"><i>q</i></span> that <span class=\"tex-span\"><i>i</i> + 2<sup class=\"upper-index\"><i>j</i></sup> + 2<sup class=\"upper-index\"><i>u</i></sup> + 2<sup class=\"upper-index\"><i>q</i></sup> ≤ <i>n</i></span>, and so on ...</p><p>A corresponding sequence of powers of <span class=\"tex-span\">2</span> should be found for each element <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>. Evidently, that overall complexity of this process is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Now we need to calculate an answer. It can be done, for example, like that: we will store the array <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> — the change of the answer at the transition from <span class=\"tex-span\"><i>i</i></span> to <span class=\"tex-span\">4<i>i</i> + 1</span>. This array is formed in a trivial way during construction of sequences of powers of twos. Then it is easy to get the answer.</p><p>The overall complexity of the solution equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ee2428a267dfbd612d43da2ffe49930b13fe87a5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><h3>An Editorial to Problem <></h3><p><a href=\"http://pastebin.com/3KYnbr3X\">Here</a> one can see author's solution.</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/178\" class=\"notice\" style=\"text-decoration: none;\">ABBYY Cup 2.0 - Hard</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-10526-4449\").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: \"10526\",\n blogEntryId: \"4435\",\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=abbyy+cup\" class=\"tag notice\" style=\"text-decoration: none;\">abbyy cup</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=hard\" class=\"tag notice\" style=\"text-decoration: none;\">hard</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=solution\" class=\"tag notice\" style=\"text-decoration: none;\">solution</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-4449\"><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'>+22</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4449\"><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/ruzana.miniakhmetova\"><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/ruzana.miniakhmetova\">\n ruzana.miniakhmetova\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=\"Apr/28/2012 18:10\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4435#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/4435#comments\">\n 3\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=\"4459\">\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 (2)</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=\"90046\" 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/yaro\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3306/avatar/7c8dd4f1bec50f39.jpg'/> </a>\n <div><a href=\"/profile/yaro\" title=\"Master yaro\" class=\"rated-user user-orange\">yaro</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Apr/28/2012 22:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-90046\" href=\"?#comment-90046\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"90046\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"17\"\r\n data-commentUserId=\"3306\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/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;\">+17</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-90046\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Aaah, the local optimization of the functional trick in D — just like a boss! Magic squares — magic solution!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-90046 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-90046 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-90046\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"730107\" 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/mickus\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1611684/avatar/a2597788bc7f3f0.jpg'/> </a>\n <div><a href=\"/profile/mickus\" title=\"Pupil mickus\" class=\"rated-user user-green\">mickus</a></div>\n </div>\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/05/2020 19:07\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-730107\" href=\"?#comment-730107\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"730107\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1611684\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-730107\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How to solve problem B2 Military Trainings?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-730107 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-730107 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-730107\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4459\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; 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{prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":899,"cells":{"problem_id":{"kind":"string","value":"180A"},"contest":{"kind":"string","value":"180"},"problem":{"kind":"string","value":"A"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A. Defragmentation"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Defragmentation</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 this problem you have to implement an algorithm to defragment your hard disk. The hard disk consists of a sequence of clusters, numbered by integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The disk has <span class=\"tex-span\"><i>m</i></span> recorded files, the <span class=\"tex-span\"><i>i</i></span>-th file occupies clusters with numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, <i>n</i><sub class=\"lower-index\"><i>i</i></sub></sub></span>. These clusters are not necessarily located consecutively on the disk, but the order in which they are given corresponds to their sequence in the file (cluster <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span> contains the first fragment of the <span class=\"tex-span\"><i>i</i></span>-th file, cluster <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span> has the second fragment, etc.). Also the disc must have one or several clusters which are free from files.</p><p>You are permitted to perform operations of copying the contents of cluster number <span class=\"tex-span\"><i>i</i></span> to cluster number <span class=\"tex-span\"><i>j</i></span> (<span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>j</i></span> must be different). Moreover, if the cluster number <span class=\"tex-span\"><i>j</i></span> used to keep some information, it is lost forever. Clusters are not cleaned, but after the defragmentation is complete, some of them are simply declared unusable (although they may possibly still contain some fragments of files).</p><p>Your task is to use a sequence of copy operations to ensure that each file occupies a contiguous area of memory. Each file should occupy a consecutive cluster section, the files must follow one after another from the beginning of the hard disk. After defragmentation all free (unused) clusters should be at the end of the hard disk. After defragmenting files can be placed in an arbitrary order. Clusters of each file should go consecutively from first to last. See explanatory examples in the notes.</p><p>Print the sequence of operations leading to the disk defragmentation. Note that <span class=\"tex-font-style-bf\">you do not have to minimize</span> the number of operations, but it should not exceed <span class=\"tex-span\">2<i>n</i></span>.</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> ≤ 200</span>) — the number of clusters and the number of files, correspondingly. Next <span class=\"tex-span\"><i>m</i></span> lines contain descriptions of the files. The first number in the line is <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 1</span>), the number of clusters occupied by the <span class=\"tex-span\"><i>i</i></span>-th file. Then follow <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, <i>n</i><sub class=\"lower-index\"><i>i</i></sub></sub></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> ≤ <i>n</i></span>). It is guaranteed that each cluster number occurs not more than once and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/179e6277f4c96272f5b7990e9663833ad354bea2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>, that is, there exists at least one unused cluster. Numbers on each line are separated by spaces. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print a single integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">0 ≤ <i>k</i> ≤ 2<i>n</i></span>) — the number of operations needed to defragment the disk. Next <span class=\"tex-span\"><i>k</i></span> lines should contain the operations' descriptions as \"<span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>j</i></span>\" (copy the contents of the cluster number <span class=\"tex-span\"><i>i</i></span> to the cluster number <span class=\"tex-span\"><i>j</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>7 2<br/>2 1 2<br/>3 3 4 5<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>7 2<br/>2 1 3<br/>3 2 4 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/>2 6<br/>3 2<br/>6 3<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's say that a disk consists of <span class=\"tex-span\">8</span> clusters and contains two files. The first file occupies two clusters and the second file occupies three clusters. Let's look at examples of correct and incorrect positions of files after defragmentation. </p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12c1b4ddb5b46e5f8beefe03fec3d3f86633aa5c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></center><p>Example 2: each file must occupy a contiguous area of memory.</p><p>Example 3: the order of files to each other is not important, at first the second file can be written, and then — the first one.</p><p>Example 4: violating the order of file fragments to each other is not allowed.</p><p>Example 5: unused clusters should be located at the end, and in this example the unused clusters are <span class=\"tex-span\">3</span>, <span class=\"tex-span\">7</span>, <span class=\"tex-span\">8</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=\"4ed3be93ba1795881911316b2b04f349\"/>\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=\"209b7d239d7ac4aac4d08e5addec8461fd09dda9\"/>\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=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_64029f79823f738fc239e59e1beddcd286d27454\">\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. Defragmentation</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</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 this problem you have to implement an algorithm to defragment your hard disk. The hard disk consists of a sequence of clusters, numbered by integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. The disk has <span class=\"tex-span\"><i>m</i></span> recorded files, the <span class=\"tex-span\"><i>i</i></span>-th file occupies clusters with numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, <i>n</i><sub class=\"lower-index\"><i>i</i></sub></sub></span>. These clusters are not necessarily located consecutively on the disk, but the order in which they are given corresponds to their sequence in the file (cluster <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span> contains the first fragment of the <span class=\"tex-span\"><i>i</i></span>-th file, cluster <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span> has the second fragment, etc.). Also the disc must have one or several clusters which are free from files.</p><p>You are permitted to perform operations of copying the contents of cluster number <span class=\"tex-span\"><i>i</i></span> to cluster number <span class=\"tex-span\"><i>j</i></span> (<span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>j</i></span> must be different). Moreover, if the cluster number <span class=\"tex-span\"><i>j</i></span> used to keep some information, it is lost forever. Clusters are not cleaned, but after the defragmentation is complete, some of them are simply declared unusable (although they may possibly still contain some fragments of files).</p><p>Your task is to use a sequence of copy operations to ensure that each file occupies a contiguous area of memory. Each file should occupy a consecutive cluster section, the files must follow one after another from the beginning of the hard disk. After defragmentation all free (unused) clusters should be at the end of the hard disk. After defragmenting files can be placed in an arbitrary order. Clusters of each file should go consecutively from first to last. See explanatory examples in the notes.</p><p>Print the sequence of operations leading to the disk defragmentation. Note that <span class=\"tex-font-style-bf\">you do not have to minimize</span> the number of operations, but it should not exceed <span class=\"tex-span\">2<i>n</i></span>.</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> ≤ 200</span>) — the number of clusters and the number of files, correspondingly. Next <span class=\"tex-span\"><i>m</i></span> lines contain descriptions of the files. The first number in the line is <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub> ≥ 1</span>), the number of clusters occupied by the <span class=\"tex-span\"><i>i</i></span>-th file. Then follow <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, 2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i>, <i>n</i><sub class=\"lower-index\"><i>i</i></sub></sub></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> ≤ <i>n</i></span>). It is guaranteed that each cluster number occurs not more than once and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/179e6277f4c96272f5b7990e9663833ad354bea2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, that is, there exists at least one unused cluster. Numbers on each line are separated by spaces. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print a single integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">0 ≤ <i>k</i> ≤ 2<i>n</i></span>) — the number of operations needed to defragment the disk. Next <span class=\"tex-span\"><i>k</i></span> lines should contain the operations' descriptions as "<span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\"><i>j</i></span>" (copy the contents of the cluster number <span class=\"tex-span\"><i>i</i></span> to the cluster number <span class=\"tex-span\"><i>j</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>7 2<br />2 1 2<br />3 3 4 5<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>7 2<br />2 1 3<br />3 2 4 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br />2 6<br />3 2<br />6 3<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's say that a disk consists of <span class=\"tex-span\">8</span> clusters and contains two files. The first file occupies two clusters and the second file occupies three clusters. Let's look at examples of correct and incorrect positions of files after defragmentation. </p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12c1b4ddb5b46e5f8beefe03fec3d3f86633aa5c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></center><p>Example 2: each file must occupy a contiguous area of memory.</p><p>Example 3: the order of files to each other is not important, at first the second file can be written, and then — the first one.</p><p>Example 4: violating the order of file fragments to each other is not allowed.</p><p>Example 5: unused clusters should be located at the end, and in this example the unused clusters are <span class=\"tex-span\">3</span>, <span class=\"tex-span\">7</span>, <span class=\"tex-span\">8</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 = 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problem_id stringlengths 2 6 | contest stringlengths 1 4 | problem stringlengths 1 3 | lang stringclasses 2
values | problem_title stringlengths 0 63 | problem_statement stringlengths 0 13.7k | page stringlengths 11.2k 95.4k | long_tags stringlengths 2 1.79k | short_tags stringlengths 2 657 | tutorial_link stringlengths 0 87 | tutorial_page stringlengths 0 1.22M |
|---|---|---|---|---|---|---|---|---|---|---|
163C | 163 | C | en | C. Conveyor | <div class="problem-statement"><div class="header"><div class="title">C. Conveyor</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="proper... |
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... | ["Sortings, orderings", "Two pointers"] | ["sortings", "two pointers", "*2100"] | https://codeforces.com/blog/entry/4187 |
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163D | 163 | D | en | D. Large Refrigerator | <div class="problem-statement"><div class="header"><div class="title">D. Large Refrigerator</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 cl... |
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... | ["Brute force"] | ["brute force", "*2900"] | https://codeforces.com/blog/entry/4187 |
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163E | 163 | E | en | E. e-Government | <div class="problem-statement"><div class="header"><div class="title">E. e-Government</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="pr... |
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... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Dfs and similar", "Dynamic programming", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc", "Trees"] | ["data structures", "dfs and similar", "dp", "strings", "trees", "*2800"] | https://codeforces.com/blog/entry/4187 |
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164A | 164 | A | en | A. Variable, or There and Back Again | <div class="problem-statement"><div class="header"><div class="title">A. Variable, or There and Back Again</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="inpu... |
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<meta name="X-Csrf-Token" content="a7112335b399f5c0c789a486f6f3b506"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dfs and similar", "Graphs"] | ["dfs and similar", "graphs", "*1700"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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164B | 164 | B | en | B. Ancient Berland Hieroglyphs | <div class="problem-statement"><div class="header"><div class="title">B. Ancient Berland Hieroglyphs</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-fi... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3dfff2f3f7daf9d494fe27ccd92e53e1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Two pointers"] | ["two pointers", "*2000"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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164C | 164 | C | en | C. Machine Programming | <div class="problem-statement"><div class="header"><div class="title">C. Machine Programming</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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="7d48acab649945c63e5ad265f3f5b685"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Graph network flows", "Graphs"] | ["flows", "graphs", "*2400"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
164D | 164 | D | en | D. Minimum Diameter | <div class="problem-statement"><div class="header"><div class="title">D. Minimum Diameter</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4505cd2cf343f983b4471b3977430f6c"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search", "Brute force"] | ["binary search", "brute force", "*3100"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
164E | 164 | E | en | E. Polycarpus and Tasks | <div class="problem-statement"><div class="header"><div class="title">E. Polycarpus and Tasks</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 ... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="8a428bdb71d6ce354e9fbc1ed83b3669"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*3100"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
165A | 165 | A | en | A. Supercentral Point | <div class="problem-statement"><div class="header"><div class="title">A. Supercentral Point</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="099afd0bfa35c3223916817589b6e249"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation"] | ["implementation", "*1000"] | https://codeforces.com/blog/entry/4124 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5f007ddabbc37efbdc89468ca32e1d59"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
165B | 165 | B | en | B. Burning Midnight Oil | <div class="problem-statement"><div class="header"><div class="title">B. Burning Midnight Oil</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 ... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="d6bc101b782793036e6d2c48a11b551f"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search", "Implementation problems, programming technics, simulation"] | ["binary search", "implementation", "*1500"] | https://codeforces.com/blog/entry/4124 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5f007ddabbc37efbdc89468ca32e1d59"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
165C | 165 | C | en | C. Another Problem on Strings | <div class="problem-statement"><div class="header"><div class="title">C. Another Problem on Strings</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"... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="bb70dda2a1a82297be46c2007209e099"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search", "Brute force", "Dynamic programming", "Mathematics including integration, differential equations, etc", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc", "Two pointers"] | ["binary search", "brute force", "dp", "math", "strings", "two pointers", "*1600"] | https://codeforces.com/blog/entry/4124 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5f007ddabbc37efbdc89468ca32e1d59"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
165D | 165 | D | en | D. Beard Graph | <div class="problem-statement"><div class="header"><div class="title">D. Beard Graph</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="pr... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="d6615b1be182f58d15920bcbf8250660"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Disjoint set union", "Trees"] | ["data structures", "dsu", "trees", "*2100"] | https://codeforces.com/blog/entry/4124 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5f007ddabbc37efbdc89468ca32e1d59"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
165E | 165 | E | en | E. Compatible Numbers | <div class="problem-statement"><div class="header"><div class="title">E. Compatible Numbers</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="47a55bb38287f2e7e205a4952d3d57aa"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Bitmasks", "Brute force", "Dfs and similar", "Dynamic programming"] | ["bitmasks", "brute force", "dfs and similar", "dp", "*2200"] | https://codeforces.com/blog/entry/4124 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5f007ddabbc37efbdc89468ca32e1d59"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
166A | 166 | A | en | A. Rank List | <div class="problem-statement"><div class="header"><div class="title">A. Rank List</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="prop... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="cb333c672f431f38ac262edc25e7c26b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search", "Implementation problems, programming technics, simulation", "Sortings, orderings"] | ["binary search", "implementation", "sortings", "*1100"] | https://codeforces.com/blog/entry/4173 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4591051d55e2377d97daa049a5d755c1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
166B | 166 | B | en | B. Polygons | <div class="problem-statement"><div class="header"><div class="title">B. Polygons</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="prope... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="1f42d61a898f5c3f06ea82e085625b48"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Geometry, computational geometry", "Sortings, orderings"] | ["geometry", "sortings", "*2100"] | https://codeforces.com/blog/entry/4173 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4591051d55e2377d97daa049a5d755c1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
166C | 166 | C | en | C. Median | <div class="problem-statement"><div class="header"><div class="title">C. Median</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="propert... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="0bbee7c2a6388ba4230473afaa9003a9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms", "Mathematics including integration, differential equations, etc", "Sortings, orderings"] | ["greedy", "math", "sortings", "*1500"] | https://codeforces.com/blog/entry/4173 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4591051d55e2377d97daa049a5d755c1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
166D | 166 | D | en | D. Shoe Store | <div class="problem-statement"><div class="header"><div class="title">D. Shoe Store</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="pro... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="05e53aba1b1b2892d193e5f93fec8d4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Graph matchings, K\u00f6nig's theorem, vertex cover of bipartite graph", "Greedy algorithms", "Sortings, orderings", "Two pointers"] | ["dp", "graph matchings", "greedy", "sortings", "two pointers", "*2500"] | https://codeforces.com/blog/entry/4173 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4591051d55e2377d97daa049a5d755c1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
166E | 166 | E | en | E. Tetrahedron | <div class="problem-statement"><div class="header"><div class="title">E. Tetrahedron</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="pr... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5c2f611b1f54240a8169b514c9c38bc5"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Mathematics including integration, differential equations, etc", "Matrix multiplication, determinant, Cramer's rule, systems of linear equations"] | ["dp", "math", "matrices", "*1500"] | https://codeforces.com/blog/entry/4173 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4591051d55e2377d97daa049a5d755c1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
167A | 167 | A | en | A. Wizards and Trolleybuses | <div class="problem-statement"><div class="header"><div class="title">A. Wizards and Trolleybuses</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><d... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="41016c26f430ec56b9632585a9a81ead"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"] | ["implementation", "math", "*1600"] | https://codeforces.com/blog/entry/4214 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="672828db83af389a88c961e73572a092"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
167B | 167 | B | en | B. Wizards and Huge Prize | <div class="problem-statement"><div class="header"><div class="title">B. Wizards and Huge Prize</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="79dc7f089ce22e4fd128ee8ca8736259"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Mathematics including integration, differential equations, etc", "Probabilities, expected values, statistics, random variables, etc"] | ["dp", "math", "probabilities", "*1800"] | https://codeforces.com/blog/entry/4214 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="672828db83af389a88c961e73572a092"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
167C | 167 | C | en | C. Wizards and Numbers | <div class="problem-statement"><div class="header"><div class="title">C. Wizards and 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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="234b11355bb3a600dad1b6e88fbd6cea"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Games, Sprague\u2013Grundy theorem", "Mathematics including integration, differential equations, etc"] | ["games", "math", "*2300"] | https://codeforces.com/blog/entry/4214 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="672828db83af389a88c961e73572a092"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
167D | 167 | D | en | D. Wizards and Roads | <div class="problem-statement"><div class="header"><div class="title">D. Wizards and Roads</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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="aeaae58b84dd6f4c067b1944393b627b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Divide and Conquer", "Graph matchings, K\u00f6nig's theorem, vertex cover of bipartite graph", "Graphs", "Greedy algorithms"] | ["data structures", "divide and conquer", "graph matchings", "graphs", "greedy", "*3000"] | https://codeforces.com/blog/entry/4214 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="672828db83af389a88c961e73572a092"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
167E | 167 | E | en | E. Wizards and Bets | <div class="problem-statement"><div class="header"><div class="title">E. Wizards and Bets</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 clas... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="fe45614c0c1c08735c353cd387458974"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dfs and similar", "Graphs", "Mathematics including integration, differential equations, etc", "Matrix multiplication, determinant, Cramer's rule, systems of linear equations"] | ["dfs and similar", "graphs", "math", "matrices", "*2900"] | https://codeforces.com/blog/entry/4214 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="672828db83af389a88c961e73572a092"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
168A | 168 | A | en | A. Wizards and Demonstration | <div class="problem-statement"><div class="header"><div class="title">A. Wizards and 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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="43147bd8d7f26f7d87d8fdc1c1ce2591"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"] | ["implementation", "math", "*900"] | https://codeforces.com/blog/entry/4217 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f4222d863356ab8f618bdc38d61e0535"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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168B | 168 | B | en | B. Wizards and Minimal Spell | <div class="problem-statement"><div class="header"><div class="title">B. Wizards and Minimal Spell</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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="604e23b44b1636ea5282271637383e72"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"] | ["implementation", "strings", "*1700"] | https://codeforces.com/blog/entry/4217 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f4222d863356ab8f618bdc38d61e0535"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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168C | 168 | C | en | C. Wizards and Trolleybuses | <div class="problem-statement"><div class="header"><div class="title">C. Wizards and Trolleybuses</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><d... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="0073c21fe96f7de45aa2dda5a497c85d"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"] | ["implementation", "math", "*1600"] | https://codeforces.com/blog/entry/4217 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f4222d863356ab8f618bdc38d61e0535"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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168D | 168 | D | en | D. Wizards and Huge Prize | <div class="problem-statement"><div class="header"><div class="title">D. Wizards and Huge Prize</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="0294639c4ab0df38aa89c88f6bccab62"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Mathematics including integration, differential equations, etc", "Probabilities, expected values, statistics, random variables, etc"] | ["dp", "math", "probabilities", "*1800"] | https://codeforces.com/blog/entry/4217 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f4222d863356ab8f618bdc38d61e0535"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
168E | 168 | E | en | E. Wizards and Numbers | <div class="problem-statement"><div class="header"><div class="title">E. Wizards and 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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="471b3319ef391a79979324481192ece4"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Games, Sprague\u2013Grundy theorem", "Mathematics including integration, differential equations, etc"] | ["games", "math", "*2300"] | https://codeforces.com/blog/entry/4217 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f4222d863356ab8f618bdc38d61e0535"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
169A | 169 | A | en | A. Chores | <div class="problem-statement"><div class="header"><div class="title">A. Chores</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="propert... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="e562a7abf54b08d9e3c5b2ed2db702b1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Sortings, orderings"] | ["sortings", "*800"] | https://codeforces.com/blog/entry/4187 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b1ac486ac08c553b8c63f99a0a3469d8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
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169B | 169 | B | en | B. Replacing Digits | <div class="problem-statement"><div class="header"><div class="title">B. Replacing Digits</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 clas... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9fb6323e19da6dfad190cc1e7fa1f4df"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms"] | ["greedy", "*1100"] | https://codeforces.com/blog/entry/4187 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b1ac486ac08c553b8c63f99a0a3469d8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
169C | 169 | C | en | C. Substring and Subsequence | <div class="problem-statement"><div class="header"><div class="title">C. Substring and 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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="41497de8f35c1bc37109cdecf7681646"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming"] | ["dp", "*1700"] | https://codeforces.com/blog/entry/4187 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b1ac486ac08c553b8c63f99a0a3469d8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
169D | 169 | D | en | D. Lemmings | <div class="problem-statement"><div class="header"><div class="title">D. Lemmings</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="proper... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="66506e05e0d85459f96b68e93db7c9d2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2000"] | https://codeforces.com/blog/entry/4187 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b1ac486ac08c553b8c63f99a0a3469d8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
169E | 169 | E | en | E. Conveyor | <div class="problem-statement"><div class="header"><div class="title">E. Conveyor</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="proper... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="bad26b86312b0162958b212ab37eafbe"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2100"] | https://codeforces.com/blog/entry/4187 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b1ac486ac08c553b8c63f99a0a3469d8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171A | 171 | A | en | A. Mysterious numbers - 1 | <div class="problem-statement"><div class="header"><div class="title">A. Mysterious numbers - 1</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="37ce111398e69eb8974fcd7a45e880e8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Constructive algorithms"] | ["*special problem", "constructive algorithms", "*1200"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171B | 171 | B | en | B. Star | <div class="problem-statement"><div class="header"><div class="title">B. Star</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-... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="82581a5a0d12a81646dd23abcd039a9b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Combinatorics"] | ["*special problem", "combinatorics", "*1300"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171C | 171 | C | en | C. A Piece of Cake | <div class="problem-statement"><div class="header"><div class="title">C. A Piece of Cake</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... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="24463d8c80a3249463298821a19f9304"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Implementation problems, programming technics, simulation"] | ["*special problem", "implementation", "*2000"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171D | 171 | D | en | D. Broken checker | <div class="problem-statement"><div class="header"><div class="title">D. Broken checker</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b172553228da80cca4006472f25470dd"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Brute force"] | ["*special problem", "brute force", "*1300"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171E | 171 | E | en | E. MYSTERIOUS LANGUAGE | <div class="problem-statement"><div class="header"><div class="title">E. MYSTERIOUS 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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="a33941a7ade5260c071d65882d0aa34d"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc."] | ["*special problem", "*2000"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171F | 171 | F | en | F. ucyhf | <div class="problem-statement"><div class="header"><div class="title">F. ucyhf</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>64 megabytes</div><div class="input-file"><div class="property-... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3dd1fe5e93018303f6df465e424c6845"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Brute force", "Implementation problems, programming technics, simulation", "Number theory: Euler function, GCD, divisibility, etc"] | ["*special problem", "brute force", "implementation", "number theory", "*1600"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171G | 171 | G | en | G. Mysterious numbers - 2 | <div class="problem-statement"><div class="header"><div class="title">G. Mysterious numbers - 2</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="c8b68807204b298aece1a19fc7b92754"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc."] | ["*special problem", "*1600"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
171H | 171 | H | en | H. A polyline | <div class="problem-statement"><div class="header"><div class="title">H. A 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="pro... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="8dc0069222766fcab579b6d96ebf2e28"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Implementation problems, programming technics, simulation"] | ["*special problem", "implementation", "*1700"] | https://codeforces.com/blog/entry/4255 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="95fc715350206393e9f06bc0fd3eabf9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
172A | 172 | A | en | A. Phone Code | <div class="problem-statement"><div class="header"><div class="title">A. Phone Code</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="pro... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4b24654505ee26757348ac40fa2a7dc3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Brute force", "Implementation problems, programming technics, simulation"] | ["*special problem", "brute force", "implementation", "*800"] | ||
172B | 172 | B | en | B. Pseudorandom Sequence Period | <div class="problem-statement"><div class="header"><div class="title">B. Pseudorandom Sequence Period</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-fil... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="5a379e2f8501597d675db0347df136c4"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Implementation problems, programming technics, simulation", "Number theory: Euler function, GCD, divisibility, etc"] | ["*special problem", "implementation", "number theory", "*1200"] | ||
172C | 172 | C | en | C. Bus | <div class="problem-statement"><div class="header"><div class="title">C. Bus</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-ti... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="be9f6bf322f550c2175f788c39e89697"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Implementation problems, programming technics, simulation", "Sortings, orderings"] | ["*special problem", "implementation", "sortings", "*1500"] | ||
172D | 172 | D | en | D. Calendar Reform | <div class="problem-statement"><div class="header"><div class="title">D. Calendar Reform</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... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="425e0dfa27dfdd3ba627c54d2c717ce1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Number theory: Euler function, GCD, divisibility, etc"] | ["*special problem", "number theory", "*1500"] | ||
172E | 172 | E | en | E. BHTML+BCSS | <div class="problem-statement"><div class="header"><div class="title">E. BHTML+BCSS</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="pro... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="0485e2d85d4006b8f0673124ba17ebc8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Special solving requirements, e.g. unknown programming language, etc.", "Dfs and similar", "Parsing expression grammar"] | ["*special problem", "dfs and similar", "expression parsing", "*2200"] | ||
173A | 173 | A | en | A. Rock-Paper-Scissors | <div class="problem-statement"><div class="header"><div class="title">A. Rock-Paper-Scissors</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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9207a4307756fe5337f6567865a00893"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"] | ["implementation", "math", "*1300"] | https://codeforces.com/blog/entry/4289 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3300ca74d4382dba1905b54116e2e886"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
173B | 173 | B | en | B. Chamber of Secrets | <div class="problem-statement"><div class="header"><div class="title">B. Chamber of Secrets</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="07e9bee7541aa5aee3352805a412344d"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dfs and similar", "Shortest paths on weighted and unweighted graphs"] | ["dfs and similar", "shortest paths", "*1800"] | https://codeforces.com/blog/entry/4289 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3300ca74d4382dba1905b54116e2e886"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
173C | 173 | C | en | C. Spiral Maximum | <div class="problem-statement"><div class="header"><div class="title">C. Spiral Maximum</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="2fdc6b063148288ef88da1ae99ea2bc2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force", "Dynamic programming"] | ["brute force", "dp", "*1900"] | https://codeforces.com/blog/entry/4289 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3300ca74d4382dba1905b54116e2e886"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
173D | 173 | D | en | D. Deputies | <div class="problem-statement"><div class="header"><div class="title">D. Deputies</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="prope... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="a139644cb6ad4f7cb5126b6d29dcc680"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Constructive algorithms", "Graphs", "Greedy algorithms", "Implementation problems, programming technics, simulation"] | ["constructive algorithms", "graphs", "greedy", "implementation", "*2500"] | https://codeforces.com/blog/entry/4289 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3300ca74d4382dba1905b54116e2e886"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
173E | 173 | E | en | E. Camping Groups | <div class="problem-statement"><div class="header"><div class="title">E. Camping Groups</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="8befb7618389c09308d59d781eb97412"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Sortings, orderings"] | ["data structures", "sortings", "*2600"] | https://codeforces.com/blog/entry/4289 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3300ca74d4382dba1905b54116e2e886"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
174A | 174 | A | en | A. Problem About Equation | <div class="problem-statement"><div class="header"><div class="title">A. Problem About Equation</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3c23083273a4b396894c4a81582326ee"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Mathematics including integration, differential equations, etc"] | ["math", "*1100"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
174B | 174 | B | en | B. File List | <div class="problem-statement"><div class="header"><div class="title">B. File List</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="prop... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9ac7c2f2763087accca06e3f17ec9493"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Greedy algorithms", "Implementation problems, programming technics, simulation"] | ["dp", "greedy", "implementation", "*1400"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
174C | 174 | C | en | C. Range Increments | <div class="problem-statement"><div class="header"><div class="title">C. Range Increments</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 clas... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="61d9db59d148ddca61fd0511485842b0"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Greedy algorithms"] | ["data structures", "greedy", "*1800"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
174D | 174 | D | en | D. Variable, or There and Back Again | <div class="problem-statement"><div class="header"><div class="title">D. Variable, or There and Back Again</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="inpu... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f5c9d4e371cb8802436671d07676a55b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Graphs"] | ["graphs", "*1700"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
174E | 174 | E | en | E. Ancient Berland Hieroglyphs | <div class="problem-statement"><div class="header"><div class="title">E. Ancient Berland Hieroglyphs</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-fi... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="90f5e8d4843a4272138a98c4bc7fd08c"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2000"] | https://codeforces.com/blog/entry/4303 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="f8539b4f84c368e0f04723c04d0da3b3"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175A | 175 | A | en | A. Robot Bicorn Attack | <div class="problem-statement"><div class="header"><div class="title">A. Robot Bicorn Attack</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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9431da0b4bb1ca182294e9a7671872c7"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force", "Implementation problems, programming technics, simulation"] | ["brute force", "implementation", "*1400"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175B | 175 | B | en | B. Plane of Tanks: Pro | <div class="problem-statement"><div class="header"><div class="title">B. Plane of Tanks: Pro</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 c... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3646c1f715992c9759b75c1e1ad03fed"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation"] | ["implementation", "*1400"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175C | 175 | C | en | C. Geometry Horse | <div class="problem-statement"><div class="header"><div class="title">C. Geometry Horse</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="503a027d46159ca1d082fe998218e25a"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms", "Implementation problems, programming technics, simulation", "Sortings, orderings", "Two pointers"] | ["greedy", "implementation", "sortings", "two pointers", "*1600"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175D | 175 | D | en | D. Plane of Tanks: Duel | <div class="problem-statement"><div class="header"><div class="title">D. Plane of Tanks: Duel</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 ... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="57125abf2522c1649c721a665333309e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force", "Dynamic programming", "Mathematics including integration, differential equations, etc", "Probabilities, expected values, statistics, random variables, etc"] | ["brute force", "dp", "math", "probabilities", "*2400"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175E | 175 | E | en | E. Power Defence | <div class="problem-statement"><div class="header"><div class="title">E. Power Defence</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="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="2013447b61c8a78d661fe9d387e9e31b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force", "Dynamic programming", "Geometry, computational geometry", "Greedy algorithms"] | ["brute force", "dp", "geometry", "greedy", "*2600"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
175F | 175 | F | en | F. Gnomes of Might and Magic | <div class="problem-statement"><div class="header"><div class="title">F. Gnomes of Might and Magic</div><div class="time-limit"><div class="property-title">time limit per test</div>8 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="cbef161ba295d08ec017206929d1dc74"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Graphs", "Implementation problems, programming technics, simulation", "Shortest paths on weighted and unweighted graphs"] | ["data structures", "graphs", "implementation", "shortest paths", "*3000"] | https://codeforces.com/blog/entry/4339 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6310623ffb5bb2dbb605f7f81999235e"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
176A | 176 | A | en | A. Trading Business | <div class="problem-statement"><div class="header"><div class="title">A. Trading Business</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 clas... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="c210758810d636eb2416e4d8637333fd"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms", "Sortings, orderings"] | ["greedy", "sortings", "*1200"] | https://codeforces.com/blog/entry/4372 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="15679b166c86ee80065b195f1dc12b4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
176B | 176 | B | en | B. Word Cut | <div class="problem-statement"><div class="header"><div class="title">B. Word Cut</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="prope... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="dc5c82d1c9e6f6ff76d93e2fce964dc8"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming"] | ["dp", "*1700"] | https://codeforces.com/blog/entry/4372 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="15679b166c86ee80065b195f1dc12b4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
176C | 176 | C | en | C. Playing with Superglue | <div class="problem-statement"><div class="header"><div class="title">C. Playing with Superglue</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"><di... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="e4588006969ab72c8e20436375d86bb7"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Combinatorics", "Constructive algorithms"] | ["combinatorics", "constructive algorithms", "*2000"] | https://codeforces.com/blog/entry/4372 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="15679b166c86ee80065b195f1dc12b4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
176D | 176 | D | en | D. Hyper String | <div class="problem-statement"><div class="header"><div class="title">D. Hyper 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="p... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="6e3115cef554167442a46865041100aa"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming"] | ["dp", "*2500"] | https://codeforces.com/blog/entry/4372 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="15679b166c86ee80065b195f1dc12b4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
176E | 176 | E | en | E. Archaeology | <div class="problem-statement"><div class="header"><div class="title">E. Archaeology</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="pr... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="7ba9819ffeb3403d047236b624d525b4"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc", "Dfs and similar", "Trees"] | ["data structures", "dfs and similar", "trees", "*3100"] | https://codeforces.com/blog/entry/4372 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="15679b166c86ee80065b195f1dc12b4b"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
177A1 | 177 | A1 | en | A1. Good Matrix Elements | <div class="problem-statement"><div class="header"><div class="title">A1. Good Matrix Elements</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... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="e5197866757f51e4cc60143f20b86dad"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation"] | ["implementation", "*800"] | ||
177A2 | 177 | A2 | en | A2. Good Matrix Elements | <div class="problem-statement"><div class="header"><div class="title">A2. Good Matrix Elements</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... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="a99067262efcf37700fe6389fb115759"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation"] | ["implementation", "*800"] | ||
177B1 | 177 | B1 | en | B1. Rectangular Game | <div class="problem-statement"><div class="header"><div class="title">B1. Rectangular 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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="2fc98613256310a5911cf4f9b74a34ee"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Number theory: Euler function, GCD, divisibility, etc"] | ["number theory", "*1000"] | ||
177B2 | 177 | B2 | en | B2. Rectangular Game | <div class="problem-statement"><div class="header"><div class="title">B2. Rectangular 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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="fea6eca23b997a6933eda8d38c0cedb0"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Number theory: Euler function, GCD, divisibility, etc"] | ["number theory", "*1200"] | ||
177C1 | 177 | C1 | en | C1. Party | <div class="problem-statement"><div class="header"><div class="title">C1. Party</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="propert... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="d76936a275bb130bb180f52061ac580c"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dfs and similar", "Disjoint set union", "Graphs"] | ["dfs and similar", "dsu", "graphs", "*1500"] | ||
177C2 | 177 | C2 | en | C2. Party | <div class="problem-statement"><div class="header"><div class="title">C2. Party</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="propert... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="50e116fea7a3f507d6cfd15ca0a6b071"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force", "Dfs and similar", "Disjoint set union", "Graphs"] | ["brute force", "dfs and similar", "dsu", "graphs", "*1500"] | ||
177D1 | 177 | D1 | en | D1. Encrypting Messages | <div class="problem-statement"><div class="header"><div class="title">D1. Encrypting Messages</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 ... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b81400f0580807a64a9a84b89efece22"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Brute force"] | ["brute force", "*1200"] | ||
177D2 | 177 | D2 | en | D2. Encrypting Messages | <div class="problem-statement"><div class="header"><div class="title">D2. Encrypting Messages</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 ... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="48c462f942119313327e019f62540af4"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Heaps, binary search trees, segment trees, hash tables, etc"] | ["data structures", "*1500"] | ||
177E1 | 177 | E1 | en | E1. Space Voyage | <div class="problem-statement"><div class="header"><div class="title">E1. Space Voyage</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="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b75bf5635a383d49877f152a06780a56"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search"] | ["binary search", "*1700"] | ||
177E2 | 177 | E2 | en | E2. Space Voyage | <div class="problem-statement"><div class="header"><div class="title">E2. Space Voyage</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="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="1f66a11ce4267ec7c3bb692fbf306f66"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Binary search"] | ["binary search", "*1900"] | ||
177F1 | 177 | F1 | en | F1. Script Generation | <div class="problem-statement"><div class="header"><div class="title">F1. Script Generation</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="14630b066306802cdf1095736c5f4b56"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1800"] | ||
177F2 | 177 | F2 | en | F2. Script Generation | <div class="problem-statement"><div class="header"><div class="title">F2. Script Generation</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="2d892dccc2f9d63a425dc7e21e849c2a"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2300"] | ||
177G1 | 177 | G1 | en | G1. Fibonacci Strings | <div class="problem-statement"><div class="header"><div class="title">G1. Fibonacci Strings</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="560b12aeb15e0319d215d93d809e3ff1"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"] | ["strings", "*2400"] | ||
177G2 | 177 | G2 | en | G2. Fibonacci Strings | <div class="problem-statement"><div class="header"><div class="title">G2. Fibonacci Strings</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 cl... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="480676150eefea3838ff608d49970098"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Matrix multiplication, determinant, Cramer's rule, systems of linear equations", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"] | ["matrices", "strings", "*2600"] | ||
178A1 | 178 | A1 | en | A1. Educational Game | <div class="problem-statement"><div class="header"><div class="title">A1. Educational 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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="29e4033622f39f6146b8705bd9635303"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1000"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178A2 | 178 | A2 | en | A2. Educational Game | <div class="problem-statement"><div class="header"><div class="title">A2. Educational 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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="acc6766b611b248ece56a3894f20ccaf"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms"] | ["greedy", "*1000"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178A3 | 178 | A3 | en | A3. Educational Game | <div class="problem-statement"><div class="header"><div class="title">A3. Educational 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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="33e792d50f6191dded5eaf691120a310"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Greedy algorithms"] | ["greedy", "*1100"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178B1 | 178 | B1 | en | B1. Greedy Merchants | <div class="problem-statement"><div class="header"><div class="title">B1. Greedy Merchants</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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9dd932d6dc7a4d8bc484ae9aaaf59681"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1600"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178B2 | 178 | B2 | en | B2. Greedy Merchants | <div class="problem-statement"><div class="header"><div class="title">B2. Greedy Merchants</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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="503f21e50028a71154335775f2170c2d"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1600"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178B3 | 178 | B3 | en | B3. Greedy Merchants | <div class="problem-statement"><div class="header"><div class="title">B3. Greedy Merchants</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 cla... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="70b91f6f1920b99470c26725023c09ae"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1800"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178C1 | 178 | C1 | en | C1. Smart Beaver and Resolving Collisions | <div class="problem-statement"><div class="header"><div class="title">C1. Smart Beaver and Resolving Collisions</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="d7e086a122b6ff0e22a3c63dab10f918"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1600"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178C2 | 178 | C2 | en | C2. Smart Beaver and Resolving Collisions | <div class="problem-statement"><div class="header"><div class="title">C2. Smart Beaver and Resolving Collisions</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="ea0d258f82c98eb1274e9a7f079cea8a"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1900"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178C3 | 178 | C3 | en | C3. Smart Beaver and Resolving Collisions | <div class="problem-statement"><div class="header"><div class="title">C3. Smart Beaver and Resolving Collisions</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="19cdd833207c329937ed965bbeb4e603"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2000"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178D1 | 178 | D1 | en | D1. Magic Squares | <div class="problem-statement"><div class="header"><div class="title">D1. Magic Squares</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="3ff812c7266680b7d4b424b55092e934"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1500"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178D2 | 178 | D2 | en | D2. Magic Squares | <div class="problem-statement"><div class="header"><div class="title">D2. Magic Squares</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="966cbd5fbff8539dae49826503c04498"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1900"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178D3 | 178 | D3 | en | D3. Magic Squares | <div class="problem-statement"><div class="header"><div class="title">D3. Magic Squares</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=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="1028ba0d7a7c05b541a9779570fdc879"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2100"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178E1 | 178 | E1 | en | E1. The Beaver's Problem - 2 | <div class="problem-statement"><div class="header"><div class="title">E1. The Beaver's Problem - 2</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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="673023c9fd4cd49195ea57a5c80753d5"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1900"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178E2 | 178 | E2 | en | E2. The Beaver's Problem - 2 | <div class="problem-statement"><div class="header"><div class="title">E2. The Beaver's Problem - 2</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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="b68bb1b375947bc6df19df7175b92fd9"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2000"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178E3 | 178 | E3 | en | E3. The Beaver's Problem - 2 | <div class="problem-statement"><div class="header"><div class="title">E3. The Beaver's Problem - 2</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">... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="afbaf70d3ff90a3327174da4877dff39"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2300"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178F1 | 178 | F1 | en | F1. Representative Sampling | <div class="problem-statement"><div class="header"><div class="title">F1. Representative Sampling</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"><... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="278c95f03a621abfca6316cd25ce4a61"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*1800"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178F2 | 178 | F2 | en | F2. Representative Sampling | <div class="problem-statement"><div class="header"><div class="title">F2. Representative Sampling</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"><... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="0ca27c26988481a28ae3eb0377061101"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Dynamic programming", "Sortings, orderings", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"] | ["dp", "sortings", "strings", "*2200"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
178F3 | 178 | F3 | en | F3. Representative Sampling | <div class="problem-statement"><div class="header"><div class="title">F3. Representative Sampling</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"><... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="71fcc7a81b429cefd00568a9c6639c8a"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | [] | ["*2500"] | https://codeforces.com/blog/entry/4435 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="9803a8c876621fb05b7814936ddb10a2"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... |
180A | 180 | A | en | A. Defragmentation | <div class="problem-statement"><div class="header"><div class="title">A. Defragmentation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class=... |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="X-Csrf-Token" content="4ed3be93ba1795881911316b2b04f349"/>
<meta id="viewport" name="viewport" content="width=device-width, initial-scale=0.01"/>
... | ["Implementation problems, programming technics, simulation"] | ["implementation", "*1800"] |
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