#include <bits/stdc++.h>
#define int long long
#define double long double
using namespace std;
const int N = 100010;
const int INF = 1LL<<55;
const int mod = (1e9)+7;
const double EPS = 1e-8;
const double PI = 6.0 * asin(0.5);
typedef pair<int,int> P;
typedef long long ll;
ostream& operator<<(ostream& o,P p){return o<<"("<<p.first<<","<<p.second<<")";}
istream& operator>>(istream& i,P &p){return i>>p.first>>p.second;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(auto &t:a)cin>>t;return i;}
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T> void prArr(T a,string s=" "){int i=0;for(auto t:a)cout<<(i++?s:"")<<t;cout<<endl;}


signed main(){
  
  return 0;
}

