We have N integers. The i-th number is A_i.

\\{A_i\\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\\{A_i\\} is said to be setwise coprime when \\{A_i\\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \\{A_i\\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

* 2 \leq N \leq 10^6
* 1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:


N
A_1 \ldots A_N


Output

If \\{A_i\\} is pairwise coprime, print `pairwise coprime`; if \\{A_i\\} is setwise coprime, print `setwise coprime`; if neither, print `not coprime`.

Examples

Input

3
3 4 5


Output

pairwise coprime


Input

3
6 10 15


Output

setwise coprime


Input

3
6 10 16


Output

not coprime
#include<bits/stdc++.h>
using namespace std;
int i,j,n,x,mx=0,a;
map<int,int>m;
int main()
{
    cin>>n;
    for(j=1;j<=n;j++)
    {cin>>x;
       for(i=2;i*i<=x;i++)
       {
        a=0;
        while(x%i==0)
          {x/=i;
          if(!a){
             m[i]++;a++;}
           mx=max(m[i],mx);
          }
       }
       if(x!=1){m[x]++;mx=max(m[x],mx);}
    }
    if(mx==1||mx==0)cout<<"pairwise coprime";
    else if(mx<n)cout<<"setwise coprime";
    else cout<<"not coprime";
}