#include<iostream>
#include<stdio.h>
#include<string>
#include<cstring>
#include<vector>
#include<stack>
#include<algorithm>
#include<queue>
using namespace std;
#define clr(a, x) memset(a, x, sizeof(a))
#define mp(x, y) make_pair(x, y)
#define pb(x) push_back(x)
#define X first
#define Y second
#define fastin                    \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);
typedef long long LL;
typedef pair<int, int> PII;
typedef vector<int> VI;
const int INF=0x3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-6;