text: #include <iostream>
  #include <cstdio>
  #include <vector>
  #include <queue>
  #include <stack>
  #include <algorithm>
  #include <set>
  #include <map>
  #include <deque>
  #include <cmath>
  #include <string>
  #include <iomanip>
  #include <locale>
  #include <list>
  #include <bitset>
  #include <tuple>
  #include <fstream>
  using namespace std;
   
  #define FORN(i,m,n) for(int i=(m); i<int(n); ++i)
  #define PRINTARR(a,n) FORN(i,0,n) cout<<a[i]<<" "; cout<<endl
  #define PRINTVEC(v) FORN(i,0,v.size()) cout<<v[i]<<" "; cout<<endl
  #define PRINTMAT(m) FORN(j,0,m.size()) {PRINTVEC(m[j]);}
  
  typedef long long ll;
  
  const int inf = 1e9 + 9;
  const int ms = 1e5 + 5;
  
  int main(){
    ios_base::sync_with_stdio(false); cin.tie(NULL);
  }
  