//#pragma GCC optimize("O2147483647")
//#pragma GCC optimize("inline")
//#pragma GCC optimize("-ffast-math")
// #pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("inline-small-functions")
//#pragma GCC optimize("-finline-small-functions")
//#pragma GCC optimize("-fexpensive-optimizations")
//#pragma GCC optimize("-funsafe-loop-optimizations")
//#pragma GCC optimize("inline-functions-called-once")
//#pragma GCC target("sse,sse2,sse3,sse3,sse4,popcnt,abm,mmx,avx")
//#pragma GCC optimze("fast-math")
#define GLIBCXX_DEBUG
#include <bits/stdc++.h>
//#include "testlib.h"
#define rep(i, j, k) for (int i = (int)(j); i<(int)(k); i++)
#define per(i, j, k) for (int i = (int)(k); i>=(int)(j); i++)
#define For(i, n) rep(i, 0, n)
#define Goe(i, a) for (auto& i: a)
#define pb push_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)((x).size())
#define deb(a) cout << "\t" << #a << " = " << (a) << "\n"
#define deb2(a, b) cout << "\t" << #a << " = " << (a) << "\t" << #b << " = " << (b) << "\n"
#define fprd fprintf(stderr,
#define fi first
#define se second
#define endl '\n'
using namespace std;
typedef long long ll;
//#define int ll
typedef vector<int> vi;
typedef pair<int, int> pi;
typedef vector<pi> vpi;

int main() {

}