1714 B君的游戏(Nim博弈)

1714 B君的游戏

基准时间限制：1 秒 空间限制：131072 KB 分值: 40 难度：4级算法题

B君和L君要玩一个游戏。刚开始有n个正整数  ai  。

双方轮流操作。每次操作，选一个正整数x，将其移除，再添加7个数字  x1,x2...x7  。要求对于  xi  ，满足  0<=xi<x  且  x&xi=xi

注意0不能被选取，所以这个游戏一定会结束，而谁无法操作谁就失败。
B君根据自己的经验，认为先手胜率高一点，所以B君是先手。
B君想知道自己是否必胜。

Input

第一行一个整数n (1 <= n <= 100000) 以下n行n个数ai (0 <= a_i < 2^64)

Output

如果先手必胜，输出"B"，否则输出"L"。

Input示例

4

1

2

3

4

Output示例

B

//尼姆博弈的变形，sg 值很容易想到，然后异或和即可，坑点在于卡读入

 # include <cstdio>
 # include <cstring>
 # include <cstdlib>
 # include <iostream>
 # include <vector>
 # include <queue>
 # include <stack>
 # include <map>
 # include <bitset>
 # include <sstream>
 # include <set>
 # include <cmath>
 # include <algorithm>
 # pragma  comment(linker,"/STACK:102400000,102400000")
 using namespace std;
 # define LL          long long
 # define pr          pair
 # define mkp         make_pair
 # define lowbit(x)   ((x)&(-x))
 # define PI          acos(-1.0)
 # define INF         0x3f3f3f3f
 # define eps         1e-
 # define MOD         

 namespace fastIO{
     #define BUF_SIZE 100000
     #define OUT_SIZE 100000
     #define ll long long
     //fread->read
     bool IOerror=;
     inline char nc(){
         static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
         if (p1==pend){
             p1=buf; pend=buf+fread(buf,,BUF_SIZE,stdin);
             if (pend==p1){IOerror=;return -;}
             //{printf("IO error!\n");system("pause");for (;;);exit(0);}
         }
         return *p1++;
     }
     inline bool blank(char ch){return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';}
     inline void read(int &x){
         bool sign=; char ch=nc(); x=;
         for (;blank(ch);ch=nc());
         if (IOerror)return;
         if (ch=='-')sign=,ch=nc();
         for (;ch>=''&&ch<='';ch=nc())x=x*+ch-'';
         if (sign)x=-x;
     }
     inline void read(ll &x){
         bool sign=; char ch=nc(); x=;
         for (;blank(ch);ch=nc());
         if (IOerror)return;
         if (ch=='-')sign=,ch=nc();
         for (;ch>=''&&ch<='';ch=nc())x=x*+ch-'';
         if (sign)x=-x;
     }
     inline void read(double &x){
         bool sign=; char ch=nc(); x=;
         for (;blank(ch);ch=nc());
         if (IOerror)return;
         if (ch=='-')sign=,ch=nc();
         for (;ch>=''&&ch<='';ch=nc())x=x*+ch-'';
         if (ch=='.'){
             double tmp=; ch=nc();
             for (;ch>=''&&ch<='';ch=nc())tmp/=10.0,x+=tmp*(ch-'');
         }
         if (sign)x=-x;
     }
     inline void read(char *s){
         char ch=nc();
         for (;blank(ch);ch=nc());
         if (IOerror)return;
         for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch;
         *s=;
     }
     inline void read(char &c){
         for (c=nc();blank(c);c=nc());
         if (IOerror){c=-;return;}
     }
     //getchar->read
     inline void read1(int &x){
         char ch;int bo=;x=;
         for (ch=getchar();ch<''||ch>'';ch=getchar())if (ch=='-')bo=;
         for (;ch>=''&&ch<='';x=x*+ch-'',ch=getchar());
         if (bo)x=-x;
     }
     inline void read1(ll &x){
         char ch;int bo=;x=;
         for (ch=getchar();ch<''||ch>'';ch=getchar())if (ch=='-')bo=;
         for (;ch>=''&&ch<='';x=x*+ch-'',ch=getchar());
         if (bo)x=-x;
     }
     inline void read1(double &x){
         char ch;int bo=;x=;
         for (ch=getchar();ch<''||ch>'';ch=getchar())if (ch=='-')bo=;
         for (;ch>=''&&ch<='';x=x*+ch-'',ch=getchar());
         if (ch=='.'){
             double tmp=;
             for (ch=getchar();ch>=''&&ch<='';tmp/=10.0,x+=tmp*(ch-''),ch=getchar());
         }
         if (bo)x=-x;
     }
     inline void read1(char *s){
         char ch=getchar();
         for (;blank(ch);ch=getchar());
         for (;!blank(ch);ch=getchar())*s++=ch;
         *s=;
     }
     inline void read1(char &c){for (c=getchar();blank(c);c=getchar());}
     //scanf->read
     inline void read2(int &x){scanf("%d",&x);}
     inline void read2(ll &x){
         #ifdef _WIN32
             scanf("%I64d",&x);
         #else
         #ifdef __linux
             scanf("%lld",&x);
         #else
             puts("error:can't recognize the system!");
         #endif
         #endif
     }
     inline void read2(double &x){scanf("%lf",&x);}
     inline void read2(char *s){scanf("%s",s);}
     inline void read2(char &c){scanf(" %c",&c);}
     inline void readln2(char *s){gets(s);}
     //fwrite->write
     struct Ostream_fwrite{
         char *buf,*p1,*pend;
         Ostream_fwrite(){buf=new char[BUF_SIZE];p1=buf;pend=buf+BUF_SIZE;}
         void out(char ch){
             if (p1==pend){
                 fwrite(buf,,BUF_SIZE,stdout);p1=buf;
             }
             *p1++=ch;
         }
         void print(int x){
             static char s[],*s1;s1=s;
             if (!x)*s1++='';if (x<)out('-'),x=-x;
             while(x)*s1++=x%+'',x/=;
             while(s1--!=s)out(*s1);
         }
         void println(int x){
             static char s[],*s1;s1=s;
             if (!x)*s1++='';if (x<)out('-'),x=-x;
             while(x)*s1++=x%+'',x/=;
             while(s1--!=s)out(*s1); out('\n');
         }
         void print(ll x){
             static char s[],*s1;s1=s;
             if (!x)*s1++='';if (x<)out('-'),x=-x;
             while(x)*s1++=x%+'',x/=;
             while(s1--!=s)out(*s1);
         }
         void println(ll x){
             static char s[],*s1;s1=s;
             if (!x)*s1++='';if (x<)out('-'),x=-x;
             while(x)*s1++=x%+'',x/=;
             while(s1--!=s)out(*s1); out('\n');
         }
         void print(double x,int y){
             static ll mul[]={,,,,,,,,,
                 ,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL,
                 100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL};
             if (x<-1e-)out('-'),x=-x;x*=mul[y];
             ll x1=(ll)floor(x); if (x-floor(x)>=0.5)++x1;
             ll x2=x1/mul[y],x3=x1-x2*mul[y]; print(x2);
             if (y>){out('.'); for (size_t i=;i<y&&x3*mul[i]<mul[y];out(''),++i); print(x3);}
         }
         void println(double x,int y){print(x,y);out('\n');}
         void print(char *s){while (*s)out(*s++);}
         void println(char *s){while (*s)out(*s++);out('\n');}
         void flush(){if (p1!=buf){fwrite(buf,,p1-buf,stdout);p1=buf;}}
         ~Ostream_fwrite(){flush();}
     }Ostream;
     inline void print(int x){Ostream.print(x);}
     inline void println(int x){Ostream.println(x);}
     inline void print(char x){Ostream.out(x);}
     inline void println(char x){Ostream.out(x);Ostream.out('\n');}
     inline void print(ll x){Ostream.print(x);}
     inline void println(ll x){Ostream.println(x);}
     inline void print(double x,int y){Ostream.print(x,y);}
     inline void println(double x,int y){Ostream.println(x,y);}
     inline void print(char *s){Ostream.print(s);}
     inline void println(char *s){Ostream.println(s);}
     inline void println(){Ostream.out('\n');}
     inline void flush(){Ostream.flush();}
     //puts->write
     char Out[OUT_SIZE],*o=Out;
     inline void print1(int x){
         static char buf[];
         char *p1=buf;if (!x)*p1++='';if (x<)*o++='-',x=-x;
         while(x)*p1++=x%+'',x/=;
         while(p1--!=buf)*o++=*p1;
     }
     inline void println1(int x){print1(x);*o++='\n';}
     inline void print1(ll x){
         static char buf[];
         char *p1=buf;if (!x)*p1++='';if (x<)*o++='-',x=-x;
         while(x)*p1++=x%+'',x/=;
         while(p1--!=buf)*o++=*p1;
     }
     inline void println1(ll x){print1(x);*o++='\n';}
     inline void print1(char c){*o++=c;}
     inline void println1(char c){*o++=c;*o++='\n';}
     inline void print1(char *s){while (*s)*o++=*s++;}
     inline void println1(char *s){print1(s);*o++='\n';}
     inline void println1(){*o++='\n';}
     inline void flush1(){if (o!=Out){if (*(o-)=='\n')*--o=;puts(Out);}}
     struct puts_write{
         ~puts_write(){flush1();}
     }_puts;
     inline void print2(int x){printf("%d",x);}
     inline void println2(int x){printf("%d\n",x);}
     inline void print2(char x){printf("%c",x);}
     inline void println2(char x){printf("%c\n",x);}
     inline void print2(ll x){
         #ifdef _WIN32
             printf("%I64d",x);
         #else
         #ifdef __linux
             printf("%lld",x);
         #else
             puts("error:can't recognize the system!");
         #endif
         #endif
     }
     inline void println2(ll x){print2(x);printf("\n");}
     inline void println2(){printf("\n");}
     #undef ll
     #undef OUT_SIZE
     #undef BUF_SIZE
 };
 using namespace fastIO;
 # define MX
 /**************************/
 int main()
 {
     LL n;
     fastIO::read(n);
     //scanf("%lld",&n);
     LL sg = ;
     for (int i=;i<=n;i++)
     {
         LL sb;
         fastIO::read(sb);
         //scanf("%lld",&sb);
         LL pp=;

         while (sb)
         {
             if (sb&(1LL)) pp++;
             sb/=;
         }

         sg^=*(pp-);
     }

     if (sg==)
         printf("L\n");
     else
         printf("B\n");
     return ;
 }