text: // clang-format off
  #include<bits/stdc++.h>
  // g++ -std=c++17 -Wl,-stack_size -Wl,0x10000000 main.cpp
  #define mp make_pair
  #define pu push_back
  #define INF 1000000001
  #define MOD 1000000007
  #define EPS 1e-6
  #define ll long long int
  #define ld long double
  #define fi first
  #define se second
  #define t1(x)                cerr<<#x<<" : "<<x<<endl
  #define t2(x, y)             cerr<<#x<<" : "<<x<<" "<<#y<<" : "<<y<<endl
  #define t3(x, y, z)          cerr<<#x<<" : " <<x<<" "<<#y<<" : "<<y<<" "<<#z<<" : "<<z<<endl
  #define t4(a,b,c,d)          cerr<<#a<<" : "<<a<<" "<<#b<<" : "<<b<<" "<<#c<<" : "<<c<<" "<<#d<<" : "<<d<<endl
  #define t5(a,b,c,d,e)          cerr<<#a<<" : "<<a<<" "<<#b<<" : "<<b<<" "<<#c<<" : "<<c<<" "<<#d<<" : "<<d<<" "<<#e<<" : "<<e<<endl
  #define t6(a,b,c,d,e,f)          cerr<<#a<<" : "<<a<<" "<<#b<<" : "<<b<<" "<<#c<<" : "<<c<<" "<<#d<<" : "<<d<<" "<<#e<<" : "<<e<<" "<<#f<<" : "<<f<<endl
  #define GET_MACRO(_1,_2,_3,_4,_5,_6,NAME,...) NAME
  #define t(...) GET_MACRO(__VA_ARGS__,t6,t5, t4, t3, t2, t1)(__VA_ARGS__)
  #define _ cerr<<"here"<<endl;
  #define __ {ios::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);}
  
  using namespace std;
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  template <ll> ostream& operator<<(ostream& os, const vector<ll>& v) { os << "["; for (int i = 0; i < v.size(); ++i) { if(v[i]!=INF) os << v[i]; else os << "INF";if (i != v.size() - 1) os << ", "; } os << "]"; return os; } 
  template<class A, class B> ostream& operator<<(ostream& out, const pair<A, B> &a){ return out<<"("<<a.first<<", "<<a.second<<")";}
  template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) { os << "["; for (int i = 0; i < v.size(); ++i) { os << v[i]; ;if (i != v.size() - 1) os << ", "; } os << "]"; return os; } 
  template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {os << "{"; for(auto it : s) {if(it != *s.rbegin()) os << it << ", "; else os << it;} os << "}"; return os;}
  // clang-format on
  
  int main() {
      __;
  
      return 0;
  }
  