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 <iostream>
using namespace std;
int n,a,d,t[1000003],maxa=-(1<<30);
int gcd(int x,int y)
{
    if(!y) return x;
    return gcd(y,x%y);
}
void fj(int x)
{
    for(int i=2;i*i<=x;)
	{
        if(!(x%i)){
            t[i]++;
            while(!(x%i)) x/=i;
        }
        else i++;
    }
    if(x>1) t[x]++;
}
int main()
{
    cin>>n>>a;
    d=a;
    for(int i=2;i<=n;i++)
	{
        cin>>a;
        if(maxa<a) maxa=a;
        d=gcd(d,a);
        fj(a);
    }
    if(d==1){
        for(int i=2;i<=maxa;i++)
            if(t[i]>1)
			{
				cout<<"setwise coprime";return 0;
			}
        cout<<"pairwise coprime";
    }
    else cout<<"not coprime";
    return 0;
}