#include<bits/stdc++.h>
//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<stdio.h>
#include<algorithm>
#include<queue>
#include<string.h>
#include<iostream>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<iomanip>
#include<bitset>
using namespace std; //
#define ll long long
#define pb push_back
#define FOR(a) for(int i=1;i<=a;i++)
#define sqr(a) (a)*(a)
#define dis(a,b) sqrt(sqr(a.x-b.x)+sqr(a.y-b.y))
ll qp(ll a,ll b,ll mod){ll t=1;while(b){if(b&1)t=t*a%mod;b>>=1;a=a*a%mod;}return t;}
struct DOT{int x;int y;};
inline void read(int &x){int k=0;char f=1;char c=getchar();for(;!isdigit(c);c=getchar())if(c=='-')f=-1;for(;isdigit(c);c=getchar())k=k*10+c-'0';x=k*f;}
const int dx[4]={0,0,-1,1};
const int dy[4]={1,-1,0,0};
const int inf=0x3f3f3f3f;
const ll mod=1e9+7;
const int maxn=1e5+5; //----------------------maxn----------------------//
