text: //user snippet for competiitve coding 
  
  #include <bits/stdc++.h>
  using namespace std;
  
  #define pb push_back
  #define MOD 1000000007 
  
  long long fast_expo(int base,int exp){
  	long long res =1;
  	while(exp>0){
  		if(exp%2==1){
  			res=(res*base)%MOD;
  		}	base=(base*base)%MOD;
  			exp/=2;
  		
  	}	
  	return res%MOD;
  }
  
  //short hand for usual tokens
  #define pb push_back
  #define fi first
  #define se second
  #define ls last 
  
  #define all(x) (x).begin(), (x).end() //Forward traversal
  #define rall(x) (x).rbegin, (x).rend() //reverse traversal
  
  // traversal function to avoid long template definition. Now with C++11 auto alleviates the pain.
  #define tr(c,i) for(__typeof__((c)).begin() i = (c).begin(); i != (c).end(); i++)
  
  // find if a given value is present in a container. Container version. Runs in log(n) for set and map
  #define present(c,x) ((c).find(x) != (c).end())
  
  //find version works for all containers. This is present in std namespace.
  #define cpresent(c,x) (find(all(c),x) != (c).end())
  
  // Avoiding wrap around of size()-1 where size is a unsigned int.
  #define sz(a) int((a).size())
  
  
  using namespace std;
  
  // Shorthand for commonly used types
  typedef vector<int> vi;
  typedef vector<vi> vvi;
  typedef pair<int, int> ii;
  typedef vector<ii> vii;
  typedef long long ll;
  typedef vector<ll> vll;
  typedef vector<vll> vvll;
  typedef double ld;
  
  
  int main() {
      ios::sync_with_stdio(false);
      cin.tie(0);
      cout.precision(10);
      
  
  
  
  
  
  
      return 0;
  }
  
  