#include <bits/stdc++.h>
#define Trang main
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define ALL(x) x.begin(), x.end()
#define RALL(x) x.rbegin(), x.rend()
#define el cout<<"\n";
using namespace std;
const int MAXN = 1e5 + 5;
template<typename T>
void TT(initializer_list<T> li) {
    for(const auto& x : li) {cout << x << " ";}
}
mt19937_64 rd(chrono::steady_clock().now().time_since_epoch().count());

Trang(void) {
    ios_base::sync_with_stdio(0); 
    cin.tie(0); cout.tie(0);
    if(fopen("TASK.inp", "r")) {
        freopen("TASK.inp", "r", stdin);
        freopen("TASK.out", "w", stdout);
    }

    return 0;
}
// T.T<33~~