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#include<cstdio>  
#include<iostream>  
#include<algorithm>  
#include<cstdlib>  
#include<cstring>
#include<string>
#include<climits>
#include<vector>
#include<cmath>
#include<map>
#define LL long long
 
using namespace std;
 
inline char nc(){
    /* 
  static char buf[100000],*p1=buf,*p2=buf;
  if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }
  return *p1++;
    */return getchar();
}
 
inline void read(int &x){
  char c=nc();int b=1;
  for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
  for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;
}
 
inline void read(LL &x){
  char c=nc();LL b=1;
  for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
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