Template

#include <bits/stdc++.h>
#define inp1(x) scanf("%d",&x)
#define inp2(x,y) scanf("%d %d",&x,&y)
#define Unique(v) v.resize(unique(v.begin(),v.end())-v.begin())
#define Sort(v) sort(v.begin(),v.end(),greater<int>());
#define fread() freopen("inp.txt","r",stdin)
#define fwrite() freopen("out.txt","w",stdout)
#define mem(n,m) memset(n,m,sizeof n)
int Set(int N,int pos){return N=N | (1<<pos);}
int reset(int N,int pos){return N= N & ~(1<<pos);}
bool check(int N,int pos){return (bool)(N & (1<<pos));}
int cnt_leading_zero_bits(int N){return __builtin_clz(N);}
int cnt_trailing_zero_bits(int N){return __builtin_ctz(N);}
int cnt_no_of_bits_on(long long N){return __builtin_popcountll(N);}
int mod_of_negative_number(int n,int m){return ((n%m)+m)%m;}
//catalan(n+1)=(2*(2*n+1)*catalan(n))/(n+2) ... catalan(0)=1
//priority_queue< int, vector<int>, greater<int> > PQ;// keeps in ascending order
// bool operator < ( const node& b ) const