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<cstdio>
#include<algorithm>
using namespace std;
const int maxn=1e6+5;
const int INF=0x3f3f3f3f;
int num[maxn];
int main()
{
    int n;
    scanf("%d",&n);
    bool pairwise=true,setwise=true;
    for(int i=1;i<=n;i++)
    {
        int a;
        scanf("%d",&a);
        for(int j=2;j*j<=a;j++)
        {
            int cnt=0;
            for(;a%j==0;a/=j) cnt++;
            if(cnt) num[j]++;
        }
        if(a>1) num[a]++;
    }
    for(int i=1;i<=1000000;i++)
    {
        if(num[i]>1) pairwise=false;
        if(num[i]==n) setwise=false;
    }
    if(pairwise) puts("pairwise coprime");
    else if(setwise) puts("setwise coprime");
    else puts("not coprime");
    return 0;
}
