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;
const int N = 2e6;

#define Maxn 1000000	

int n, a[N], vis[N];

int main() {
	scanf("%d", &n);
	for(int i = 1;i <= n; ++i) scanf("%d", &a[i]), vis[a[i]] += 1;
	int A = 1, B = 0;
	for(int j = 2;j <= Maxn; ++j) {
		int num = j, tmp = 0;
		for(int i = num; i <= Maxn; i += num)
			if(vis[i])
				tmp += vis[i];
		if(tmp > 1) B = 1;
		if(tmp == n) A = 0;
	}
	if(A == 0) puts("not coprime");
	else if(B == 1) puts("setwise coprime");
	else puts("pairwise coprime");
	return 0;
}