#include "bits/stdc++.h"
using namespace std;
template<typename typC,typename typD> istream & operator>>(istream &cin,pair<typC,typD> &a) {return cin>>a.first>>a.second;}
template<typename typC> istream & operator>>(istream &cin,vector<typC> &a){for (auto &x:a) cin>>x;return cin;}
template<typename typC,typename typD> ostream & operator<<(ostream &cout,const pair<typC,typD> &a) {return cout<<a.first<<' '<<a.second;}
template<typename typC,typename typD> ostream & operator<<(ostream &cout,const vector<pair<typC,typD>> &a){for (auto &x:a) cout<<x<<'\n';return cout;}
template<typename typC> ostream & operator<<(ostream &cout,const vector<typC> &a){int n=a.size();if (!n) return cout;cout<<a[0];for (int i=1;i<n;i++) cout<<' '<<a[i];return cout;}
#define x first
#define y second
typedef long long LL;
typedef pair<int, int> PII;
const int N = 100010, INF = 2e9, mod = 1e9 + 7;

int main()
{
    ios::sync_with_stdio(0);cin.tie(0);



    return 0;
}