#define

/*||||||||||||||||||||||||||||||||||       
||    ||\      //||     ||   //   ||      
||    ||\\    // ||     ||  //    || 
||    || \\  //  ||     || //     || 
||    ||  \\//   ||     ||//      || 
||    ||   \/    ||     ||\\      ||
||    ||         ||     || \\     ||
||    ||         ||     ||  \\    ||
||    ||         ||     ||   \\   ||
||||||||||||||||||||||||||||||||||*/

#include <bits/stdc++.h>
#define MOD 1000000007
#define test int t; cin>>t; while(t--)
#define init(arr,val) memset(arr,val,sizeof(arr))
#define loop(i,a,b) for(int i=a;i<b;i++)
#define loopr(i,a,b) for(int i=a;i>=b;i--)
#define loops(i,a,b,step) for(int i=a;i<b;i+=step)
#define looprs(i,a,b,step) for(int i=a;i>=b;i-=step)
#define ull unsigned long long int
#define ll long long int
#define P pair
#define PLL pair<long long, long long>
#define PII pair<int, int>
#define PUU pair<unsigned long long int, unsigned long long int>
#define L list
#define V vector
#define D deque
#define ST set
#define MS multiset
#define M map
#define UM unordered_map
#define mp make_pair
#define pb push_back
#define pf push_front
#define MM multimap
#define F first
#define S second
#define IT iterator
#define RIT reverse_iterator
#define FAST ios_base::sync_with_stdio(false);cin.tie();cout.tie();
#define FILE_READ_IN freopen("input.txt","r",stdin);
#define FILE_READ_OUT freopen("output.txt","w",stdout);
#define MAXN 25


//Now I don't think they are important