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 gcd(int x,int y)
{
	return y?gcd(y,x%y):x;
}
int n,fir,sec,cnt[1000001]; 
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int a;
		scanf("%d",&a);
		cnt[a]++;
		sec=gcd(sec,a);
	}
	for(int i=2;i<=1000000;i++)
	{
		int sum=0;
		for(int l=i;l<=1000000;l+=i)
			sum+=cnt[l];
		if(sum>1)
		{
			fir=1;
			break;
		}
	}
	cout<<(fir?sec==1?"setwise coprime":"not coprime":"pairwise coprime");
	return 0;
}