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;
long long int n,a[1000001];
int gcd(int c,int d) {
	return d==0?c:gcd(d,c%d);
}
int main() {
	cin>>n;
	int ans=0;
	for (int i=0; i<n; i++) {
		int x;
		cin>>x;
		a[x]++;
		ans=gcd(ans,x);
	}
	int ok=1;
	for (int i=2; i<=1000000; i++) {
		int cnt=0;
		for (int j=i; j<=1000000; j+=i)
			cnt+=a[j];
		if (cnt>1) ok=0;
	}
	if (ok) cout<<"pairwise coprime"<<endl;
	else if (ans==1) cout<<"setwise coprime"<<endl;
	else cout<<"not coprime";

	return 0;
}