#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 TT(s, i) cout<<s<<": "<<i<<"\n";
#define el cout<<"\n";
using namespace std;
const int MAXN = 1e5 + 5;
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);

    cerr << "\n__rtv__";
    return 0;
}
// T.T<33~~