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;
const int N = 1e6+5;
int num[N]={0};
int main()
{
    int n,x,ok=0,cnt=0;
    scanf("%d",&n);
    for(int j=1;j<=n;j++)
    {
        scanf("%d",&x);
        for(int i=2;i<=x/i;i++)
            {
                 if(x%i==0)num[i]++;
                 while(x%i==0)
                 {
                     x/=i;
                 }
            }
             if(x>1)
                num[x]++;
    }
    for(int i=1;i<=N;i++)
    {
        if(num[i]>1)ok=1;
        cnt=max(cnt,num[i]);
    }
    if(ok==0)printf("pairwise coprime\n");
    else if(cnt<n) printf("setwise coprime\n");
    else
                printf("not coprime\n");
    return 0;
}
