#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, s, n) for (ll i = (s); i <= (ll)(n); i++)
typedef long long ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;
typedef vector<vector<vector<string>>> vvvs;
typedef vector<char> vc;
typedef vector<vector<char>> vvc;
typedef vector<vector<vector<char>>> vvvc;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef vector<double> vd;
typedef vector<vector<double>> vvd;
typedef vector<vector<vector<double>>> vvvd;
#define yes(ans) if(ans)cout << "yes"<< endl; else cout << "no" << endl
#define Yes(ans) if(ans)cout << "Yes"<< endl; else cout << "No" << endl
#define YES(ans) if(ans)cout << "YES"<< endl ;else cout << "NO" << endl
#define all1(x) x.begin(),x.end()
#define all2(x) x.rbegin(), x.rend()
#define so(x) sort(all1(x))
#define re(x) reverse(all1(x))
#define rso(x) sort(all2(x))
#define vco(x, a) count(all1(x), a)
#define per(x) next_permutation(all1(x))

int main(){
    return 0;
}