{"id":952,"date":"2014-08-30T11:52:26","date_gmt":"2014-08-30T03:52:26","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=952"},"modified":"2016-08-26T23:46:23","modified_gmt":"2016-08-26T15:46:23","slug":"bestcoder-round-7-solution","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/bestcoder-round-7-solution\/","title":{"rendered":"BestCoder Round #7 Solution"},"content":{"rendered":"<p><!--more--><\/p>\n<p><a target=\"_blank\" href=\"https:\/\/i.minus.com\/iiz0ufNWly1II.jpg\"><br \/>\n<img decoding=\"async\" class=\"aligncenter size-full wp-image-1391\" src=\"https:\/\/i.minus.com\/iiz0ufNWly1II.jpg\" border=\"0\"\/><br \/>\n<\/a><br \/>\n\u3002\u7ec8 Board\u3002\u3002\u3002\u3002\u606d\u559c\u675c\u6559\u53d6\u5f97 #7 \u7684\u51a0\u519b\u3002\u3002\u867d\u7136\u6ca1\u6709 AK\u3002\u3002\u8fd8\u662f\u88ab\u5979\u5f97\u5230\u4e86\u300axxx \u5199\u771f\u96c6\u300b\u3002\u3002\u3002\u3002\u300204 \u6700\u7ec8\u4e09\u4e2a\u7a0b\u5e8f\u901a\u8fc7\u3002\u30022 \u4e2a\u6811\u5957\u6811\u4e00\u4e2a\u5206\u5757\uff08Java \u7684\uff09\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u6ce8\uff1a04 \u7684 <code>pretest<\/code> \u548c <code>systest<\/code> \u4e00\u6837\u4f46\u5c45\u7136\u8fd8\u6709 RP \u7206\u70b8 fst \u7684\u3002\uff08\u5361\u8fc7\u4e86 pre \u6ca1\u5361\u8fc7 systest\u3002\u3002\u3002\uff09\u3002\u3002\u3002\u3002\u3002<\/p>\n<p><a href=\"http:\/\/bestcoder.hdu.edu.cn\/contests\/contest_show.php?cid=531\">http:\/\/bestcoder.hdu.edu.cn\/contests\/contest_show.php?cid=531<\/a><\/p>\n<h2>1001 Little Pony and Permutation<\/h2>\n<h3>\u9898\u610f\uff1a<\/h3>\n<p>\u6c42\u4e00\u4e2a\u5faa\u73af\u7684\u5faa\u73af\u5206\u89e3\u3002<\/p>\n<h3>\u5206\u6790\uff1a<\/h3>\n<p>\u76f4\u63a5 while \u5faa\u73af\u641e\u641e\u5c31\u597d\u4e86\u3002<\/p>\n<h2>1002 Little Pony and Alohomora Part I<\/h2>\n<p><a href=\"http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4986\">http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4986<\/a><\/p>\n<h3>\u9898\u610f\uff1a<\/h3>\n<p>\u6c42\u968f\u673a\u6392\u5217\u7684\u671f\u671b\u5faa\u73af\u4e2a\u6570\u3002<\/p>\n<h3>\u5206\u6790\uff1a<\/h3>\n<p>\u3010\u5f15\u7406 1\u3011\u5bf9\u4e8e\u4e00\u4e2a\u968f\u673a\u6392\u5217\u7684\u67d0\u4e2a\u5143\u7d20\uff0c\u5904\u5728\u4e00\u4e2a\u957f\u5ea6\u4e3a $$k$$ \u7684\u5faa\u73af\u4e2d\u7684\u6982\u7387\u4e3a $$1\/n$$\uff08\u4e0e\u5faa\u73af\u7684\u957f\u5ea6\u65e0\u5173\uff09\u3002<\/p>\n<p>\u8bc1\u660e\uff1a<br \/>\n\u65b9\u6cd5\u4e00\uff1a<br \/>\n\u8003\u5bdf\u67d0\u4e2a\u5143\u7d20\u5904\u5728\u957f\u5ea6\u4e3a $k$ \u7684\u5faa\u73af\u4e2d\u7684\u65b9\u6848\u6570\uff0c\u6709\uff1a<\/p>\n<p>$$!\\binom{n-1}{k-1}(k-1)!(n-k)! = (n-1)! $$<\/p>\n<p>\u6bd4\u4e0a\u603b\u7684\u65b9\u6848\u6570\u5f97\u5230\u6982\u7387:<\/p>\n<p>$$!\\frac{(n-1)!}{n!} = \\frac{1}{n}$$<\/p>\n<p>\u65b9\u6cd5\u4e8c\uff1a<br \/>\n\u3002\u3002\u3002<br \/>\n\u6211\u4eec\u53ef\u4ee5\u7528\u7b2c\u4e00\u9898\u7684\u65b9\u6cd5\uff0c\u5c06\u6bcf\u4e2a\u6392\u5217\u5199\u6210 <code>Cycle Notation<\/code>\uff0c\u5e76\u5c06\u6bcf\u4e2a\u5faa\u73af\u4e2d\u6700\u5c0f\u7684\u5143\u7d20\u653e\u5728\u672b\u5c3e\u3002<br \/>\n\u90a3\u4e48\u6bcf\u4e00\u4e2a\u6392\u5217\u7684 <code>Cycle Notation<\/code> \u548c\u53e6\u4e00\u4e2a\u6392\u5217\u53ef\u4ee5\u5efa\u7acb\u8d77\u4e00\u4e00\u5bf9\u5e94\u3002\u800c 1 \u5904\u5728\u7684\u5faa\u73af\u4e2d\u7684\u957f\u5ea6\u7b49\u4e8e\u5b83\u5728\u6392\u5217\u4e2d\u7684\u4f4d\u7f6e\uff0c\u56e0\u6b64\u6240\u6709\u957f\u5ea6\u7684\u6982\u7387\u90fd\u662f $$\\frac{1}{n}$$\u3002<\/p>\n<p>\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/p>\n<p>\u8003\u8651 dp \u3002\u3002\u8bbe e[n] \u8868\u793a\u957f\u5ea6\u4e3a n \u7684\u6392\u5217\u7684\u5faa\u73af\u4e2a\u6570\u7684\u671f\u671b\u3002\u3002\u6211\u4eec\u679a\u4e3e\u5176\u4e2d\u4e00\u4e2a\u5faa\u73af\u7684\u957f\u5ea6\u3002\u6839\u636e\u671f\u671b\u53ef\u52a0\u3002\u3002\u6709\u3002\u3002\u3002<\/p>\n<p>$$!e[n] = \\frac{\\sum_{i=1}^n e[n-i]}{n} $$<br \/>\n\u4e5f\u5c31\u662f e[n] = H[n] \uff08\u8c03\u548c\u7ea7\u6570\uff09<br \/>\n\u5bf9\u4e8e\u8c03\u548c\u7ea7\u6570\uff0c\u53ef\u4ee5\u8f83\u5c0f\u9879\u66b4\u529b\uff0c\u8f83\u5927\u9879\u65f6\u7528 log() \u8fd1\u4f3c\u3002<\/p>\n<p>\uff08\u5f53\u7136\u4f3c\u4e4e<a href=\"http:\/\/www.cnblogs.com\/yuiffy\/p\/3948184.html\">\u627e\u89c4\u5f8b<\/a>\u4e5f\u80fd\u8fc7\u3002\u3002\u3002\u3002\u3002\uff09<\/p>\n<h2>1003 Little Pony and Dice<\/h2>\n<p><a href=\"http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4987\">http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4987<\/a><\/p>\n<h3>\u9898\u610f\uff1a<\/h3>\n<p>\u6709\u4e00\u4e2a $$m$$ \u9762\u7684\u5747\u5300\u9ab0\u5b50\uff08[1, $$m$$]\uff09\uff0c\u7136\u540e\u4ece 0 \u51fa\u53d1\uff0c\u6839\u636e\u6254\u7684\u6570\u5b57\uff0c\u51b3\u5b9a\u5411\u524d\u8d70\u7684\u6b65\u6570\uff0c\u8d70\u5230 $$\\geq n$$ \u65f6\u5c31\u505c\u6b62\u3002<br \/>\n\u6c42\u521a\u597d\u5728 $$n$$ \u505c\u6b62\u7684\u6982\u7387\u3002\u8981\u6c42\u8bef\u5dee $$10^{-5}$$ \u4ee5\u5185\u3002\uff08$$1\\leq m, n\\leq 10^9$$\uff09<\/p>\n<h3>\u5206\u6790\uff1a<\/h3>\n<p>\u5f53 $$m$$ \u5f88\u5927\u65f6\uff0c\u6982\u7387\u4f1a\u63a5\u8fd1 0\uff0c\u7531\u4e8e\u8bef\u5dee $$10^{-5}$$\uff0c\u5f53 $$n\\geq 600000$$ \u65f6\uff0c\u76f4\u63a5\u8fd4\u56de 0\u3002\u3002<br \/>\n\uff08\u3002\u3002\u3002$$n=m$$ \u65f6\u7684\u7b54\u6848\u7ea6\u662f $$e^{-1\/n}$$\u3002\u3002.\u56e0\u6b64\u5b9e\u9645\u8fd9\u4e2a\u503c\u5927\u7ea6\u662f 550000 \u5de6\u53f3\u3002\u3002\u3002\uff09<\/p>\n<ul>\n<li>\u5f53 $$m\\geq n$$ \u65f6\uff1a<\/li>\n<p>\u8bbe f[i] \u8868\u793a\u8ddd\u79bb n \u8fd8\u6709 i \u6b65\u65f6\u6240\u6c42\u7684\u6982\u7387\uff0c\u6709\uff1a<\/p>\n<pre>\r\nf[i] = sigma j &lt; i (dp[j])\/m\r\nf[i-1] = sigma j &lt; i-1 (dp[j])\/m\r\nf[i] - f[i-1] = dp[i-1]\/m\r\nf[i] = f[i-1]*(1+1\/m)\r\n\u521d\u503c f[1] = 1\/m\r\n<\/pre>\n<p>\u89e3\u5f97\uff1a<br \/>\n$$!f[n] = \\frac{(1+1\/m)^{n-1}}{m}$$\u3002<\/p>\n<li>\u5f53 $$m\\le n$$ \u65f6\uff1a<\/li>\n<p>\u5f53 $$n$$ \u5f88\u5927\u540e\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u503c\u4f1a\u5f88\u5feb\u6536\u655b\u7684 $$ 2\/(m+1) $$\u3002\u3002<br \/>\n\u8003\u8651 DP\uff0c\u5e76\u7528\u90e8\u5206\u548c\u4f18\u5316\u5230 $$O(n)$$\u3002<\/ul>\n<pre class=\"brush: cpp; collapse: true; light: false; title: Solution_by_xudyh.cpp; toolbar: true; notranslate\" title=\"Solution_by_xudyh.cpp\">\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cctype&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;cstdio&gt;\r\n#include &lt;cmath&gt;\r\n#include &lt;algorithm&gt;\r\n#include &lt;vector&gt;\r\n#include &lt;string&gt;\r\n#include &lt;iostream&gt;\r\n#include &lt;sstream&gt;\r\n#include &lt;map&gt;\r\n#include &lt;set&gt;\r\n#include &lt;queue&gt;\r\n#include &lt;stack&gt;\r\n#include &lt;fstream&gt;\r\n#include &lt;numeric&gt;\r\n#include &lt;iomanip&gt;\r\n#include &lt;bitset&gt;\r\n#include &lt;list&gt;\r\n#include &lt;stdexcept&gt;\r\n#include &lt;functional&gt;\r\n#include &lt;utility&gt;\r\n#include &lt;ctime&gt;\r\n#include &lt;cassert&gt;\r\n#include &lt;complex&gt;\r\nusing namespace std;\r\n#define rep(i,a,n) for (int i=a;i&lt;n;i++)\r\n#define per(i,a,n) for (int i=n-1;i&gt;=a;i--)\r\n#define pb push_back\r\n#define mp make_pair\r\n#define all(x) (x).begin(),(x).end()\r\n#define fi first\r\n#define se second\r\n#define SZ(x) ((int)(x).size())\r\n#define ACCU accumulate\r\n#define TWO(x) (1&lt;&lt;(x))\r\n#define TWOL(x) (1ll&lt;&lt;(x))\r\n#define clr(a) memset(a,0,sizeof(a))\r\n#define POSIN(x,y) (0&lt;=(x)&amp;&amp;(x)&lt;n&amp;&amp;0&lt;=(y)&amp;&amp;(y)&lt;m)\r\n#define PRINTC(x) cout&lt;&lt;&quot;Case #&quot;&lt;&lt;++__&lt;&lt;&quot;: &quot;&lt;&lt;x&lt;&lt;endl\r\n#define POP(x) (__builtin_popcount(x))\r\n#define POPL(x) (__builtin_popcountll(x))\r\ntypedef vector&lt;int&gt; VI;\r\ntypedef vector&lt;string&gt; VS;\r\ntypedef vector&lt;double&gt; VD;\r\ntypedef long long ll;\r\ntypedef long double LD;\r\ntypedef pair&lt;int,int&gt; PII;\r\ntypedef pair&lt;ll,ll&gt; PLL;\r\ntypedef vector&lt;ll&gt; VL;\r\ntypedef vector&lt;PII&gt; VPII;\r\ntypedef complex&lt;double&gt; CD;\r\nconst int inf=0x20202020;\r\nconst ll mod=1000000007;\r\nconst double eps=1e-9;\r\nconst double pi=3.1415926535897932384626;\r\nconst int DX&#x5B;]={1,0,-1,0},DY&#x5B;]={0,1,0,-1};\r\nll powmod(ll a,ll b) {ll res=1;a%=mod;for(;b;b&gt;&gt;=1){if(b&amp;1)res=res*a%mod;a=a*a%mod;}return res;}\r\nll powmod(ll a,ll b,ll mod) {ll res=1;a%=mod;for(;b;b&gt;&gt;=1){if(b&amp;1)res=res*a%mod;a=a*a%mod;}return res;}\r\nll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}\r\n\/\/ head\r\n\r\nconst int N=1000000;\r\ndouble dp&#x5B;N+100],s&#x5B;N+100];\r\nint n,m;\r\nint main() {\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    freopen(&quot;out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n    while (scanf(&quot;%d%d&quot;,&amp;m,&amp;n)!=EOF) {\r\n        if (m&gt;=600000) puts(&quot;0.00000&quot;);\r\n        else {\r\n            if (n&lt;=m) printf(&quot;%.5f\\n&quot;,pow(1+1.\/m,n-1)\/m);\r\n            else {\r\n                dp&#x5B;0]=1; s&#x5B;0]=1;\r\n                for (int i=1;i&lt;=n;i++) {\r\n                    if (i&lt;=m) dp&#x5B;i]=s&#x5B;i-1]\/m;\r\n                    else dp&#x5B;i]=(s&#x5B;i-1]-s&#x5B;i-m-1])\/m;\r\n                    s&#x5B;i]=s&#x5B;i-1]+dp&#x5B;i];\r\n                    if (i&gt;=m&amp;&amp;abs(dp&#x5B;i]-2.\/(m+1))&lt;=1e-9) { n=i;break;}\r\n                }\r\n                printf(&quot;%.5f\\n&quot;,dp&#x5B;n]);\r\n            }\r\n        }\r\n    }\r\n}\r\n<\/pre>\n<h2>1004 Little Pony and Boast Busters<\/h2>\n<p><a href=\"http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4988\">http:\/\/acm.hdu.edu.cn\/showproblem.php?pid=4988<\/a><\/p>\n<h3>\u9898\u610f\uff1a<\/h3>\n<p>\u7ed9\u5b9a\u4e0a\u4e0b\u4e24\u4e2a\u6392\u5217 <code>A[]<\/code>, <code>B[]<\/code>\uff0c\u8981\u6c42\u8be2\u95ee\u76f8\u540c\u9879\u4e4b\u95f4\u4e24\u4e24\u8fde\u7ebf\u7684\u4ea4\u53c9\u6570\uff0c\u5e76\u652f\u6301\u4ea4\u6362\u64cd\u4f5c\u3002\u3002\u3002<\/p>\n<h3>\u5206\u6790\uff1a<\/h3>\n<p>\u3002\u3002\u3002\u9759\u6001\u95ee\u9898\u5c31\u662f\u6c42\u6392\u5217 <code>P[]<\/code> \u7684\u9006\u5e8f\u5bf9\u3002\u3002<br \/>\n\u5176\u4e2d <code>P[i] = pA[B[i]]<\/code>\u3002 \uff08\u8fd9\u91cc <code>pA[]<\/code> \u662f <code>A[]<\/code> \u4e2d\u67d0\u4e2a\u5143\u7d20\u7684\u4f4d\u7f6e\u3002\u3002\u7c7b\u4f3c\u7684 <code>pB[]<\/code> \u662f <code>B[]<\/code> \u4e2d\u67d0\u4e2a\u5143\u7d20\u7684\u4f4d\u7f6e\u3002\u3002\u3002\uff09<\/p>\n<p>\u8003\u5bdf\u4ea4\u6362\u64cd\u4f5c\u3002\u3002\u65e0\u8bba\u662f\u4ea4\u6362\u4e0b\u6392\u8fd8\u662f\u4e0a\u6392\uff0c\u90fd\u53ef\u4ee5\u770b\u6210\u4ea4\u6362 <code>P[]<\/code> \u4e2d\u7684\u4e24\u9879\u3002\u3002\u3002<\/p>\n<p>\u5bf9\u4e8e\u4ea4\u6362\u4e0b\u6392\u3002\u3002\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nswap(B&#x5B;a], B&#x5B;b]); pB&#x5B;B&#x5B;a]]=a,pB&#x5B;B&#x5B;b]]=b,\r\nswap(P&#x5B;a], P&#x5B;b]);\r\n<\/pre>\n<p>\u5bf9\u4e8e\u4ea4\u6362\u4e0a\u6392\u3002\u3002\u6709\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nswap(A&#x5B;a],A&#x5B;b]); pA&#x5B;A&#x5B;a]]=a,pA&#x5B;A&#x5B;b]]=b,\r\nswap(P&#x5B;pB&#x5B;A&#x5B;a]]], P&#x5B;pB&#x5B;A&#x5B;b]]]);            \r\n<\/pre>\n<p>\u4e8e\u662f\u8f6c\u5316\u6210\u52a8\u6001\u9006\u5e8f\u5bf9\u95ee\u9898\uff0c\u652f\u6301\u4fee\u6539\u6392\u5217\u4e2d\u7684\u4efb\u610f\u4e00\u9879\u3002<br \/>\n\u52a8\u6001\u9006\u5e8f\u5bf9\u95ee\u9898\u7b49\u4ef7\u4e8e\u533a\u95f4 <code>kth<\/code> \u5927\u503c\uff08\u533a\u95f4 <code>Rank<\/code>\uff09\u95ee\u9898\u3002\u3002\u53ef\u4ee5\u7528\u7ecf\u5178\u7684\u6811\u5957\u6811\u65b9\u6cd5\u3002\u3002\u3002<br \/>\n\u3002\u3002\u590d\u6742\u5ea6 $$O(nlog^2n)$$\u3002<\/p>\n<pre class=\"brush: cpp; collapse: true; light: false; title: std_by_xiaodao.cpp; toolbar: true; notranslate\" title=\"std_by_xiaodao.cpp\">\r\n\/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: Aug. 17th 2014 **\/ \/\/{\r\n\r\n\/** Header .. **\/ \/\/{\r\n#pragma comment(linker, &quot;\/STACK:36777216&quot;)\r\n\/\/#pragma GCC optimize (&quot;O2&quot;)\r\n#define LOCAL\r\n\/\/#include &quot;testlib.h&quot;\r\n#include &lt;functional&gt;\r\n#include &lt;algorithm&gt;\r\n#include &lt;iostream&gt;\r\n#include &lt;fstream&gt;\r\n#include &lt;sstream&gt;\r\n#include &lt;iomanip&gt;\r\n#include &lt;numeric&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n#include &lt;cassert&gt;\r\n#include &lt;complex&gt;\r\n#include &lt;cstdio&gt;\r\n#include &lt;string&gt;\r\n#include &lt;vector&gt;\r\n#include &lt;bitset&gt;\r\n#include &lt;queue&gt;\r\n#include &lt;stack&gt;\r\n#include &lt;cmath&gt;\r\n#include &lt;ctime&gt;\r\n#include &lt;list&gt;\r\n#include &lt;set&gt;\r\n#include &lt;map&gt;\r\n\r\n\/\/#include &lt;tr1\/unordered_set&gt;\r\n\/\/#include &lt;tr1\/unordered_map&gt;\r\n\/\/#include &lt;array&gt;\r\n\r\nusing namespace std;\r\n\r\n#define REP(i, n) for (int i=0;i&lt;n;++i)\r\n#define FOR(i, a, b) for (int i=a;i&lt;b;++i)\r\n#define DWN(i, b, a) for (int i=b-1;i&gt;=a;--i)\r\n#define REP_1(i, n) for (int i=1;i&lt;=n;++i)\r\n#define FOR_1(i, a, b) for (int i=a;i&lt;=b;++i)\r\n#define DWN_1(i, b, a) for (int i=b;i&gt;=a;--i)\r\n#define REP_C(i, n) for (int n____=n,i=0;i&lt;n____;++i)\r\n#define FOR_C(i, a, b) for (int b____=b,i=a;i&lt;b____;++i)\r\n#define DWN_C(i, b, a) for (int a____=a,i=b-1;i&gt;=a____;--i)\r\n#define REP_N(i, n) for (i=0;i&lt;n;++i)\r\n#define FOR_N(i, a, b) for (i=a;i&lt;b;++i)\r\n#define DWN_N(i, b, a) for (i=b-1;i&gt;=a;--i)\r\n#define REP_1_C(i, n) for (int n____=n,i=1;i&lt;=n____;++i)\r\n#define FOR_1_C(i, a, b) for (int b____=b,i=a;i&lt;=b____;++i)\r\n#define DWN_1_C(i, b, a) for (int a____=a,i=b;i&gt;=a____;--i)\r\n#define REP_1_N(i, n) for (i=1;i&lt;=n;++i)\r\n#define FOR_1_N(i, a, b) for (i=a;i&lt;=b;++i)\r\n#define DWN_1_N(i, b, a) for (i=b;i&gt;=a;--i)\r\n#define REP_C_N(i, n) for (int n____=(i=0,n);i&lt;n____;++i)\r\n#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i&lt;b____;++i)\r\n#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i&gt;=a____;--i)\r\n#define REP_1_C_N(i, n) for (int n____=(i=1,n);i&lt;=n____;++i)\r\n#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i&lt;=b____;++i)\r\n#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i&gt;=a____;--i)\r\n\r\n#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)\r\n#define REP_S(i, str) for (char*i=str;*i;++i)\r\n#define REP_L(i, hd, suc) for (int i=hd;i;i=suc&#x5B;i])\r\n#define REP_G(i, u) REP_L(i,hd&#x5B;u],suc)\r\n#define REP_SS(x, s) for (int x=s;x;x=(x-1)&amp;s)\r\n#define DO(n) for ( int ____n = n; ____n--&gt;0; )\r\n#define REP_2(i, j, n, m) REP(i, n) REP(j, m)\r\n#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)\r\n#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)\r\n#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)\r\n#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)\r\n#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)\r\n\r\n#define ALL(A) A.begin(), A.end()\r\n#define LLA(A) A.rbegin(), A.rend()\r\n#define CPY(A, B) memcpy(A, B, sizeof(A))\r\n#define INS(A, P, B) A.insert(A.begin() + P, B)\r\n#define ERS(A, P) A.erase(A.begin() + P)\r\n#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())\r\n#define UBD(A, x) (upper_bound(ALL(A), x) - A.begin())\r\n#define CTN(T, x) (T.find(x) != T.end())\r\n#define SZ(A) int((A).size())\r\n#define PB push_back\r\n#define MP(A, B) make_pair(A, B)\r\n#define PTT pair&lt;T, T&gt;\r\n#define Ts *this\r\n#define rTs return Ts\r\n#define fi first\r\n#define se second\r\n#define re real()\r\n#define im imag()\r\n\r\n#define Rush for(int ____T=RD(); ____T--;)\r\n#define Display(A, n, m) {                      \\\r\n  REP(i, n){\t\t                            \\\r\n        REP(j, m-1) cout &lt;&lt; A&#x5B;i]&#x5B;j] &lt;&lt; &quot; &quot;;     \\\r\n        cout &lt;&lt; A&#x5B;i]&#x5B;m-1] &lt;&lt; endl;\t\t        \\\r\n\t}\t\t\t\t\t\t                    \\\r\n}\r\n#define Display_1(A, n, m) {                    \\\r\n\tREP_1(i, n){\t\t                        \\\r\n        REP_1(j, m-1) cout &lt;&lt; A&#x5B;i]&#x5B;j] &lt;&lt; &quot; &quot;;   \\\r\n        cout &lt;&lt; A&#x5B;i]&#x5B;m] &lt;&lt; endl;\t\t        \\\r\n\t}\t\t\t\t\t\t                    \\\r\n}\r\n\r\ntypedef long long LL;\r\n\/\/typedef long double DB;\r\ntypedef double DB;\r\ntypedef unsigned uint;\r\ntypedef unsigned long long uLL;\r\n\r\ntypedef vector&lt;int&gt; VI;\r\ntypedef vector&lt;char&gt; VC;\r\ntypedef vector&lt;string&gt; VS;\r\ntypedef vector&lt;LL&gt; VL;\r\ntypedef vector&lt;DB&gt; VF;\r\ntypedef set&lt;int&gt; SI;\r\ntypedef set&lt;string&gt; SS;\r\ntypedef map&lt;int, int&gt; MII;\r\ntypedef map&lt;string, int&gt; MSI;\r\ntypedef pair&lt;int, int&gt; PII;\r\ntypedef pair&lt;LL, LL&gt; PLL;\r\ntypedef vector&lt;PII&gt; VII;\r\ntypedef vector&lt;VI&gt; VVI;\r\ntypedef vector&lt;VII&gt; VVII;\r\n\r\ntemplate&lt;class T&gt; inline T&amp; RD(T &amp;);\r\ntemplate&lt;class T&gt; inline void OT(const T &amp;);\r\n\/\/inline int RD(){int x; return RD(x);}\r\ninline LL RD(){LL x; return RD(x);}\r\ninline DB&amp; RF(DB &amp;);\r\ninline DB RF(){DB x; return RF(x);}\r\ninline char* RS(char *s);\r\ninline char&amp; RC(char &amp;c);\r\ninline char RC();\r\ninline char&amp; RC(char &amp;c){scanf(&quot; %c&quot;, &amp;c); return c;}\r\ninline char RC(){char c; return RC(c);}\r\n\/\/inline char&amp; RC(char &amp;c){c = getchar(); return c;}\r\n\/\/inline char RC(){return getchar();}\r\n\r\ntemplate&lt;class T&gt; inline T&amp; RDD(T &amp;);\r\ninline LL RDD(){LL x; return RDD(x);}\r\n\r\ntemplate&lt;class T0, class T1&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1){RD(x0), RD(x1); return x0;}\r\ntemplate&lt;class T0, class T1, class T2&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1, T2 &amp;x2){RD(x0), RD(x1), RD(x2); return x0;}\r\ntemplate&lt;class T0, class T1, class T2, class T3&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1, T2 &amp;x2, T3 &amp;x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1, T2 &amp;x2, T3 &amp;x3, T4 &amp;x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1, T2 &amp;x2, T3 &amp;x3, T4 &amp;x4, T5 &amp;x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5, class T6&gt; inline T0&amp; RD(T0 &amp;x0, T1 &amp;x1, T2 &amp;x2, T3 &amp;x3, T4 &amp;x4, T5 &amp;x5, T6 &amp;x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}\r\ntemplate&lt;class T0, class T1&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1){OT(x0), OT(x1);}\r\ntemplate&lt;class T0, class T1, class T2&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1, const T2 &amp;x2){OT(x0), OT(x1), OT(x2);}\r\ntemplate&lt;class T0, class T1, class T2, class T3&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1, const T2 &amp;x2, const T3 &amp;x3){OT(x0), OT(x1), OT(x2), OT(x3);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1, const T2 &amp;x2, const T3 &amp;x3, const T4 &amp;x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1, const T2 &amp;x2, const T3 &amp;x3, const T4 &amp;x4, const T5 &amp;x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5, class T6&gt; inline void OT(const T0 &amp;x0, const T1 &amp;x1, const T2 &amp;x2, const T3 &amp;x3, const T4 &amp;x4, const T5 &amp;x5, const T6 &amp;x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}\r\ninline char&amp; RC(char &amp;a, char &amp;b){RC(a), RC(b); return a;}\r\ninline char&amp; RC(char &amp;a, char &amp;b, char &amp;c){RC(a), RC(b), RC(c); return a;}\r\ninline char&amp; RC(char &amp;a, char &amp;b, char &amp;c, char &amp;d){RC(a), RC(b), RC(c), RC(d); return a;}\r\ninline char&amp; RC(char &amp;a, char &amp;b, char &amp;c, char &amp;d, char &amp;e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}\r\ninline char&amp; RC(char &amp;a, char &amp;b, char &amp;c, char &amp;d, char &amp;e, char &amp;f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}\r\ninline char&amp; RC(char &amp;a, char &amp;b, char &amp;c, char &amp;d, char &amp;e, char &amp;f, char &amp;g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b){RF(a), RF(b); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b, DB &amp;c){RF(a), RF(b), RF(c); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b, DB &amp;c, DB &amp;d){RF(a), RF(b), RF(c), RF(d); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b, DB &amp;c, DB &amp;d, DB &amp;e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b, DB &amp;c, DB &amp;d, DB &amp;e, DB &amp;f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}\r\ninline DB&amp; RF(DB &amp;a, DB &amp;b, DB &amp;c, DB &amp;d, DB &amp;e, DB &amp;f, DB &amp;g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}\r\ninline void RS(char *s1, char *s2){RS(s1), RS(s2);}\r\ninline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}\r\ntemplate&lt;class T0,class T1&gt;inline void RDD(T0&amp;a, T1&amp;b){RDD(a),RDD(b);}\r\ntemplate&lt;class T0,class T1,class T2&gt;inline void RDD(T0&amp;a, T1&amp;b, T2&amp;c){RDD(a),RDD(b),RDD(c);}\r\n\r\ntemplate&lt;class T&gt; inline void RST(T &amp;A){memset(A, 0, sizeof(A));}\r\ntemplate&lt;class T&gt; inline void FLC(T &amp;A, int x){memset(A, x, sizeof(A));}\r\ntemplate&lt;class T&gt; inline void CLR(T &amp;A){A.clear();}\r\n\r\ntemplate&lt;class T0, class T1&gt; inline void RST(T0 &amp;A0, T1 &amp;A1){RST(A0), RST(A1);}\r\ntemplate&lt;class T0, class T1, class T2&gt; inline void RST(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2){RST(A0), RST(A1), RST(A2);}\r\ntemplate&lt;class T0, class T1, class T2, class T3&gt; inline void RST(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3){RST(A0), RST(A1), RST(A2), RST(A3);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4&gt; inline void RST(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5&gt; inline void RST(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5, class T6&gt; inline void RST(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5, T6 &amp;A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}\r\ntemplate&lt;class T0, class T1&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, int x){FLC(A0, x), FLC(A1, x);}\r\ntemplate&lt;class T0, class T1, class T2&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}\r\ntemplate&lt;class T0, class T1, class T2, class T3&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5, class T6&gt; inline void FLC(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5, T6 &amp;A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}\r\ntemplate&lt;class T&gt; inline void CLR(priority_queue&lt;T, vector&lt;T&gt;, less&lt;T&gt; &gt; &amp;Q){while (!Q.empty()) Q.pop();}\r\ntemplate&lt;class T&gt; inline void CLR(priority_queue&lt;T, vector&lt;T&gt;, greater&lt;T&gt; &gt; &amp;Q){while (!Q.empty()) Q.pop();}\r\ntemplate&lt;class T&gt; inline void CLR(stack&lt;T&gt; &amp;S){while (!S.empty()) S.pop();}\r\ntemplate&lt;class T&gt; inline void CLR(queue&lt;T&gt; &amp;Q){while (!Q.empty()) Q.pop();}\r\n\r\ntemplate&lt;class T0, class T1&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1){CLR(A0), CLR(A1);}\r\ntemplate&lt;class T0, class T1, class T2&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2){CLR(A0), CLR(A1), CLR(A2);}\r\ntemplate&lt;class T0, class T1, class T2, class T3&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}\r\ntemplate&lt;class T0, class T1, class T2, class T3, class T4, class T5, class T6&gt; inline void CLR(T0 &amp;A0, T1 &amp;A1, T2 &amp;A2, T3 &amp;A3, T4 &amp;A4, T5 &amp;A5, T6 &amp;A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}\r\ntemplate&lt;class T&gt; inline void CLR(T &amp;A, int n){REP(i, n) CLR(A&#x5B;i]);}\r\n\r\ntemplate&lt;class T&gt; inline bool EPT(T &amp;a){return a.empty();}\r\ntemplate&lt;class T&gt; inline T&amp; SRT(T &amp;A){sort(ALL(A)); return A;}\r\ntemplate&lt;class T, class C&gt; inline T&amp; SRT(T &amp;A, C B){sort(ALL(A), B); return A;}\r\ntemplate&lt;class T&gt; inline T&amp; RVS(T &amp;A){reverse(ALL(A)); return A;}\r\ntemplate&lt;class T&gt; inline T&amp; UNQQ(T &amp;A){A.resize(unique(ALL(A))-A.begin());return A;}\r\ntemplate&lt;class T&gt; inline T&amp; UNQ(T &amp;A){SRT(A);return UNQQ(A);}\r\n\r\n\r\n\/\/}\r\n\r\n\/** Constant List .. **\/ \/\/{\r\n\r\nconst int MOD = int(1e9) + 7;\r\nconst int INF = 0x3f3f3f3f;\r\nconst LL INFF = 0x3f3f3f3f3f3f3f3fLL;\r\nconst DB EPS = 1e-9;\r\nconst DB OO = 1e20;\r\nconst DB PI = acos(-1.0); \/\/M_PI;\r\n\r\nconst int dx&#x5B;] = {-1, 0, 1, 0};\r\nconst int dy&#x5B;] = {0, 1, 0, -1};\r\n\r\n\/\/}\r\n\r\n\/** Add On .. **\/ \/\/{\r\n\/\/ &lt;&lt;= '0. Nichi Joo ., \/\/{\r\n\r\ntemplate&lt;class T&gt; inline T&amp; checkMin(T &amp;a,const T b){if (b&lt;a) a=b;return a;}\r\ntemplate&lt;class T&gt; inline T&amp; checkMax(T &amp;a,const T b){if (a&lt;b) a=b;return a;}\r\ntemplate&lt;class T&gt; inline T&amp; checkMin(T &amp;a, T &amp;b, const T x){checkMin(a, x), checkMin(b, x);return a;}\r\ntemplate&lt;class T&gt; inline T&amp; checkMax(T &amp;a, T &amp;b, const T x){checkMax(a, x), checkMax(b, x);return a;}\r\ntemplate &lt;class T, class C&gt; inline T&amp; checkMin(T&amp; a, const T b, C c){if (c(b,a)) a = b;return a;}\r\ntemplate &lt;class T, class C&gt; inline T&amp; checkMax(T&amp; a, const T b, C c){if (c(a,b)) a = b;return a;}\r\ntemplate&lt;class T&gt; inline T min(T a, T b, T c){return min(min(a, b), c);}\r\ntemplate&lt;class T&gt; inline T max(T a, T b, T c){return max(max(a, b), c);}\r\ntemplate&lt;class T&gt; inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}\r\ntemplate&lt;class T&gt; inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}\r\ntemplate&lt;class T&gt; inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}\r\ntemplate&lt;class T&gt; inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}\r\ntemplate&lt;class T&gt; inline T sqr(T a){return a*a;}\r\ntemplate&lt;class T&gt; inline T cub(T a){return a*a*a;}\r\ntemplate&lt;class T&gt; inline T ceil(T x, T y){return (x - 1) \/ y + 1;}\r\ntemplate&lt;class T&gt; T abs(T x){return x&gt;0?x:-x;}\r\ninline int sgn(DB x){return x &lt; -EPS ? -1 : x &gt; EPS;}\r\ninline int sgn(DB x, DB y){return sgn(x - y);}\r\n\r\ninline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))\/(2*a*b);}\r\ninline DB cot(DB x){return 1.\/tan(x);};\r\ninline DB sec(DB x){return 1.\/cos(x);};\r\ninline DB csc(DB x){return 1.\/sin(x);};\r\n\r\n\/\/}\r\n\/\/ &lt;&lt;= '1. Bitwise Operation ., \/\/{\r\nnamespace BO{\r\n\r\ninline bool _1(int x, int i){return bool(x&amp;1&lt;&lt;i);}\r\ninline bool _1(LL x, int i){return bool(x&amp;1LL&lt;&lt;i);}\r\ninline LL _1(int i){return 1LL&lt;&lt;i;}\r\ninline LL _U(int i){return _1(i) - 1;};\r\n\r\ninline int reverse_bits(int x){\r\n    x = ((x &gt;&gt; 1) &amp; 0x55555555) | ((x &lt;&lt; 1) &amp; 0xaaaaaaaa);\r\n    x = ((x &gt;&gt; 2) &amp; 0x33333333) | ((x &lt;&lt; 2) &amp; 0xcccccccc);\r\n    x = ((x &gt;&gt; 4) &amp; 0x0f0f0f0f) | ((x &lt;&lt; 4) &amp; 0xf0f0f0f0);\r\n    x = ((x &gt;&gt; 8) &amp; 0x00ff00ff) | ((x &lt;&lt; 8) &amp; 0xff00ff00);\r\n    x = ((x &gt;&gt;16) &amp; 0x0000ffff) | ((x &lt;&lt;16) &amp; 0xffff0000);\r\n    return x;\r\n}\r\n\r\ninline LL reverse_bits(LL x){\r\n    x = ((x &gt;&gt; 1) &amp; 0x5555555555555555LL) | ((x &lt;&lt; 1) &amp; 0xaaaaaaaaaaaaaaaaLL);\r\n    x = ((x &gt;&gt; 2) &amp; 0x3333333333333333LL) | ((x &lt;&lt; 2) &amp; 0xccccccccccccccccLL);\r\n    x = ((x &gt;&gt; 4) &amp; 0x0f0f0f0f0f0f0f0fLL) | ((x &lt;&lt; 4) &amp; 0xf0f0f0f0f0f0f0f0LL);\r\n    x = ((x &gt;&gt; 8) &amp; 0x00ff00ff00ff00ffLL) | ((x &lt;&lt; 8) &amp; 0xff00ff00ff00ff00LL);\r\n    x = ((x &gt;&gt;16) &amp; 0x0000ffff0000ffffLL) | ((x &lt;&lt;16) &amp; 0xffff0000ffff0000LL);\r\n    x = ((x &gt;&gt;32) &amp; 0x00000000ffffffffLL) | ((x &lt;&lt;32) &amp; 0xffffffff00000000LL);\r\n    return x;\r\n}\r\n\r\ntemplate&lt;class T&gt; inline bool odd(T x){return x&amp;1;}\r\ntemplate&lt;class T&gt; inline bool even(T x){return !odd(x);}\r\ntemplate&lt;class T&gt; inline T low_bit(T x) {return x &amp; -x;}\r\ntemplate&lt;class T&gt; inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}\r\ntemplate&lt;class T&gt; inline T cover_bit(T x){T p = 1; while (p &lt; x) p &lt;&lt;= 1;return p;}\r\ntemplate&lt;class T&gt; inline int cover_idx(T x){int p = 0; while (_1(p) &lt; x ) ++p; return p;}\r\n\r\ninline int clz(int x){return __builtin_clz(x);}\r\ninline int clz(LL x){return __builtin_clzll(x);}\r\ninline int ctz(int x){return __builtin_ctz(x);}\r\ninline int ctz(LL x){return __builtin_ctzll(x);}\r\ninline int lg2(int x){return !x ? -1 : 31 - clz(x);}\r\ninline int lg2(LL x){return !x ? -1 : 63 - clz(x);}\r\ninline int low_idx(int x){return !x ? -1 : ctz(x);}\r\ninline int low_idx(LL x){return !x ? -1 : ctz(x);}\r\ninline int high_idx(int x){return lg2(x);}\r\ninline int high_idx(LL x){return lg2(x);}\r\ninline int parity(int x){return __builtin_parity(x);}\r\ninline int parity(LL x){return __builtin_parityll(x);}\r\ninline int count_bits(int x){return __builtin_popcount(x);}\r\ninline int count_bits(LL x){return __builtin_popcountll(x);}\r\n\r\n} using namespace BO;\/\/}\r\n\r\n\r\n\/\/ &lt;&lt;= '2. Number Theory .,\/\/{\r\nnamespace NT{\r\n#define gcd __gcd\r\ninline LL lcm(LL a, LL b){return a*b\/gcd(a,b);}\r\n\r\ninline void INC(int &amp;a, int b){a += b; if (a &gt;= MOD) a -= MOD;}\r\ninline int sum(int a, int b){a += b; if (a &gt;= MOD) a -= MOD; return a;}\r\n\/* \u0123\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\u057a\u00f3\ufffd int \u02b1\ufffd\ufffd\r\ninline int sum(uint a, int b){a += b; a %= MOD;if (a &lt; 0) a += MOD; return a;}\r\ninline void INC(int &amp;a, int b){a = sum(a, b);}\r\n*\/\r\n\r\ninline void DEC(int &amp;a, int b){a -= b; if (a &lt; 0) a += MOD;}\r\ninline int dff(int a, int b){a -= b; if (a &lt; 0) a  += MOD; return a;}\r\ninline void MUL(int &amp;a, int b){a = (LL)a * b % MOD;}\r\ninline int pdt(int a, int b){return (LL)a * b % MOD;}\r\n\r\ninline int gcd(int m, int n, int &amp;x, int &amp;y){\r\n\r\n    x = 1, y = 0; int xx = 0, yy = 1, q;\r\n\r\n    while (1){\r\n        q = m \/ n, m %= n;\r\n        if (!m){x = xx, y = yy; return n;}\r\n        DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));\r\n        q = n \/ m, n %= m;\r\n        if (!n) return m;\r\n        DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));\r\n    }\r\n}\r\n\r\ninline int sum(int a, int b, int c){return sum(a, sum(b, c));}\r\ninline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}\r\ninline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}\r\ninline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}\r\n\r\ninline int pow(int a, LL b){\r\n    int c(1); while (b){\r\n        if (b&amp;1) MUL(c, a);\r\n        MUL(a, a), b &gt;&gt;= 1;\r\n    }\r\n    return c;\r\n}\r\n\r\ntemplate&lt;class T&gt; inline T pow(T a, LL b){\r\n    T c(1); while (b){\r\n        if (b&amp;1) c *= a;\r\n        a *= a, b &gt;&gt;= 1;\r\n    }\r\n    return c;\r\n}\r\n\r\ntemplate&lt;class T&gt; inline T pow(T a, int b){\r\n    return pow(a, (LL)b);\r\n}\r\n\r\ninline int _I(int b){\r\n    int a = MOD, x1 = 0, x2 = 1, q; while (1){\r\n        q = a \/ b, a %= b;\r\n        if (!a) return x2;\r\n        DEC(x1, pdt(q, x2));\r\n\r\n        q = b \/ a, b %= a;\r\n        if (!b) return x1;\r\n        DEC(x2, pdt(q, x1));\r\n    }\r\n}\r\n\r\ninline void DIV(int &amp;a, int b){MUL(a, _I(b));}\r\ninline int qtt(int a, int b){return pdt(a, _I(b));}\r\n\r\n} using namespace NT;\/\/}\r\n\r\n\r\n\/\/}\r\n\r\n\r\n\/** I\/O Accelerator Interface .. **\/ \/\/{\r\n#define g (c=getchar())\r\n#define d isdigit(g)\r\n#define p x=x*10+c-'0'\r\n#define n x=x*10+'0'-c\r\n#define pp l\/=10,p\r\n#define nn l\/=10,n\r\ntemplate&lt;class T&gt; inline T&amp; RD(T &amp;x){\r\n    char c;while(!d);x=c-'0';while(d)p;\r\n    return x;\r\n}\r\ntemplate&lt;class T&gt; inline T&amp; RDD(T &amp;x){\r\n    char c;while(g,c!='-'&amp;&amp;!isdigit(c));\r\n    if (c=='-'){x='0'-g;while(d)n;}\r\n    else{x=c-'0';while(d)p;}\r\n    return x;\r\n}\r\ninline DB&amp; RF(DB &amp;x){\r\n    \/\/scanf(&quot;%lf&quot;, &amp;x);\r\n    char c;while(g,c!='-'&amp;&amp;c!='.'&amp;&amp;!isdigit(c));\r\n    if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}\r\n        else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}\r\n    else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}\r\n        else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}\r\n    return x;\r\n}\r\n#undef nn\r\n#undef pp\r\n#undef n\r\n#undef p\r\n#undef d\r\n#undef g\r\ninline char* RS(char *s){\r\n    \/\/gets(s);\r\n    scanf(&quot;%s&quot;, s);\r\n    return s;\r\n}\r\n\r\nLL last_ans; int Case; template&lt;class T&gt; inline void OT(const T &amp;x){\r\n    \/\/printf(&quot;Case #%d: &quot;, ++Case);\r\n    \/\/printf(&quot;%lld\\n&quot;, x);\r\n    \/\/printf(&quot;%.9f\\n&quot;, x);\r\n    \/\/printf(&quot;%d\\n&quot;, x);\r\n    cout &lt;&lt; x &lt;&lt; endl;\r\n    \/\/last_ans = x;\r\n}\r\n\/\/}\r\n\r\n\r\n\/\/}\/* .................................................................................................................................. *\/\r\n\r\nconst int N = int(1e5) + 9, LV = 25;\r\n\r\nnamespace SBT{\r\n    const int NN = N*LV;\r\n    int c&#x5B;2]&#x5B;NN], sz&#x5B;NN], ky&#x5B;NN], tot;\r\n#define lx l&#x5B;x]\r\n#define rx r&#x5B;x]\r\n#define l c&#x5B;d]\r\n#define r c&#x5B;!d]\r\n#define kx ky&#x5B;x]\r\n#define sx sz&#x5B;x]\r\n#define d 0\r\n    int new_node(int v = 0){\r\n        int x=++tot;lx=rx=0;\r\n        sx=1;kx=v;\r\n        return x;\r\n    }\r\n\r\n    void upd(int x){\r\n        sx=sz&#x5B;lx]+1+sz&#x5B;rx];\r\n    }\r\n#undef d\r\n    void rot(int &amp;x,int d){\r\n        int y=rx;rx=l&#x5B;y];l&#x5B;y]=x;\r\n        upd(x),upd(y),x=y;\r\n    }\r\n\r\n    void fix(int &amp;x,int d){\r\n        if (sz&#x5B;l&#x5B;lx]] &gt; sz&#x5B;rx]) rot(x,!d);\r\n        else{\r\n            if (sz&#x5B;r&#x5B;lx]] &gt; sz&#x5B;rx]) rot(lx,d),rot(x,!d);\r\n            else return;\r\n        }\r\n        d=0,fix(lx,0),fix(rx,1);\r\n        fix(x,0),fix(x,1);\r\n    }\r\n#define d 0\r\n    void Ins(int &amp;x,int v){\r\n        if(!x) x = new_node(v);\r\n        else{\r\n            ++sz&#x5B;x]; Ins(c&#x5B;v&gt;kx]&#x5B;x],v);\r\n            fix(x,v&gt;=kx);\r\n        }\r\n    }\r\n\r\n    int d_key; void Del(int &amp;x,int v){\r\n        --sx;if(kx==v||(v&lt;kx&amp;&amp;!lx)||(v&gt;kx&amp;&amp;!rx)){\r\n            if(!lx||!rx) d_key = kx, x = lx | rx;\r\n            else Del(lx,v+1), kx = d_key;\r\n        }\r\n        else Del(c&#x5B;v&gt;kx]&#x5B;x],v);\r\n    }\r\n\r\n    int Rank(int x,int v){\r\n        int z=0;while(x){\r\n            if(kx&lt;v){\r\n                z+=sz&#x5B;lx]+1;\r\n                x=rx;\r\n            }\r\n            else{\r\n                x=lx;\r\n            }\r\n        }\r\n        return z;\r\n    }\r\n\r\n    bool Find(int x,int v){\r\n        if (!x) return 0;if (kx==v) return 1;\r\n        return Find(c&#x5B;v&gt;kx]&#x5B;x],v);\r\n    }\r\n\r\n    void Init(){\r\n        tot = 0;\r\n    }\r\n\r\n#undef d\r\n#undef l\r\n#undef r\r\n#undef lx\r\n#undef rx\r\n#undef sx\r\n#undef kx\r\n};\r\n\r\nLL res;\r\nint n, m;\r\n\r\nnamespace BIT{\r\n    int C&#x5B;N];\r\n    void Ins(int x, int v){\r\n        for (;x&lt;=n;x+=low_bit(x)) SBT::Ins(C&#x5B;x],v);\r\n    }\r\n    void Del(int x, int v){\r\n        for (;x&lt;=n;x+=low_bit(x)) SBT::Del(C&#x5B;x],v);\r\n    }\r\n    int Rank(int x, int v){\r\n        int res = 0; for (;x;x^=low_bit(x)) res += SBT::Rank(C&#x5B;x],v);\r\n        return res;\r\n    }\r\n    int Count(int x){\r\n        int res = 0; for (;x;x^=low_bit(x)) res += SBT::sz&#x5B;C&#x5B;x]];\r\n        return res;\r\n    }\r\n    void Init(){\r\n        fill(C+1, C+n+1, 0);\r\n    }\r\n};\r\n\r\nint A&#x5B;N], pA&#x5B;N], B&#x5B;N], pB&#x5B;N];\r\nint P&#x5B;N];\r\n\r\nvoid Init(){\r\n    SBT::Init(); BIT::Init(); res = 0; int x;\r\n\tREP_1(i, n) pA&#x5B;++RD(A&#x5B;i])] = i;\r\n\r\n\tREP_1(i, n){\r\n        pB&#x5B;++RD(B&#x5B;i])] = i; int x = pA&#x5B;B&#x5B;i]];\r\n\t    res += i-1-BIT::Rank(n,x+1); \/\/#\r\n        BIT::Ins(i, x), P&#x5B;i] = x;\r\n\t}\r\n}\r\n\r\n#define v P&#x5B;x]\r\n#define delta ((x-1)-BIT::Rank(x,v+1)+BIT::Rank(n,v)-BIT::Rank(x,v))\r\nvoid Change(int x, int vv){\r\n    BIT::Del(x, v);\r\n    res -= delta; v = vv;\r\n    res += delta; BIT::Ins(x, v);\r\n}\r\n#undef v\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n\/\/#define a A&#x5B;x]\r\n\/\/#define delta ((x-1)-BIT::Rank(x,a+1)+BIT::Rank(n,a)-BIT::Rank(x,a))\r\n\r\n\r\n\/\/\u6c47\u7f16\u8c03\u6808\r\nint __size__ = 256 &lt;&lt; 20; \/\/ 256MB\r\nchar *__p__ = (char*)malloc(__size__) + __size__;\r\n__asm__(&quot;movl %0, %%esp\\n&quot; :: &quot;r&quot;(__p__));\r\n\r\n    while (~scanf(&quot;%d&quot;, &amp;n)){\r\n\r\n    Init();\r\n\r\n    char cmd&#x5B;9]; Rush{\r\n        RS(cmd); if (cmd&#x5B;0] == 'Q') OT(res);\r\n        else{\r\n            int p, a, b; RD(p, a, b); ++a, ++b;\r\n            if (p == 1){\r\n                swap(B&#x5B;a], B&#x5B;b]);\r\n                pB&#x5B;B&#x5B;a]]=a,pB&#x5B;B&#x5B;b]]=b,\r\n                Change(a, pA&#x5B;B&#x5B;a]]);\r\n                Change(b, pA&#x5B;B&#x5B;b]]);\r\n            }\r\n            else{\r\n                swap(A&#x5B;a],A&#x5B;b]);\r\n                pA&#x5B;A&#x5B;a]]=a,pA&#x5B;A&#x5B;b]]=b,\r\n                Change(pB&#x5B;A&#x5B;a]], a);\r\n                Change(pB&#x5B;A&#x5B;b]], b);\r\n            }\r\n\r\n            \/*REP_1(i, n){\r\n                assert(P&#x5B;i] == pA&#x5B;B&#x5B;i]]);\r\n            }*\/\r\n        }\r\n    }\r\n\r\n    }\r\n\r\n    \/\/\/\/int x, aa; RD(x, aa); BIT::Del(x, a);\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-952","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-fm","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/952","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=952"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/952\/revisions"}],"predecessor-version":[{"id":954,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/952\/revisions\/954"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}