#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <stack>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define mp make_pair
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
typedef long long ll;
typedef vector<int> VI;
typedef pair<int, int> PII;
const ll MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int MAXN = 2e9 + 7;
// head
