// I don't care
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const double eps = 1e-10;
const double PII = acos(-1);
const int N = 200010;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f;
// int dir[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
// int dir[8][2] = {{1, 0}, {1, -1}, {1, 1}, {0, 1}, {0, -1}, {-1, 1}, {-1, 0}, {-1, -1}};
// std::mt19937 rng {std::chrono::steady_clock::now().time_since_epoch().count()};

namespace DBG {
    template <class T>
    void _dbg(const char *f,T t) { cerr<<f<<'='<<t<<'\n'; }

    template <class A,class... B>
    void _dbg(const char *f,A a,B... b) {
        while (*f!=',') cerr<<*f++;
        cerr<<'='<<a<<",";
        _dbg(f+1,b...);
    }

    template <class T>
    ostream& operator << (ostream& os,const vector<T> &v) {
        os<<"[ ";
        for (const auto &x:v) os<<x<<", ";
        os<<"]";
        return os;
    }

    #define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
}

using namespace DBG;

void solve() {

}

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int t = 1;
    // std::cin >> t;

    while (t--) {
        solve();
    }

    return 0;
}