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
#pragma GCC optimize(3)
#include<bits/stdc++.h>
using namespace std;
int gcd(int a,int b)
{
	return b?gcd(b,a%b):a;
}
int n,x,num[1000005],ok=1,g;
int main()
{
	cin>>n;
	for(int i=0;i<n;++i)
	{
		scanf("%d",&x);
		++num[x];
		g=gcd(x,g);
	}
	for(int i=2;i<=1000000;++i)
	{
		int tot=0;
		for(int j=i;j<=1000000;j+=i)
		 tot+=num[j];
		if(tot>1){ok=0;break;}
	}
	if(ok) cout<<"pairwise coprime";
	else if(g==1) cout<<"setwise coprime";
	else cout<<"not coprime";
	return 0;
}