#include <bits/stdc++.h>

#define rep(i, a, n) for(int i = (a);i < (n);i++)
#define REP(i, n)    rep(i, 0, n)
#define all(e)       (e).begin(), (e).end()

#ifdef LOCAL
#define show(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl
#else
#define show(x) true
#endif

using namespace std;
using ll = long long;
template<class T>
using V = vector<T>;

template<class T, class U>
void chmin(T &t, const U u) { if (t > u) t = u; }

template<class T, class U>
void chmax(T &t, const U u) { if (t < u) t = u; }

const int INF = (1 << 30) - 1;
const ll INFL = (ll) 5e15;
const int MOD = 1e9 + 7;

int main() {


    return 0;
}