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;
typedef long long LL;
const int N = 1e6 + 100;
int n, x, ans, maxx, res, i, j, num[N];
int gcd(int a, int b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}
int main() {
	cin >> n >> ans;
	num[ans]++;
	for (i = 2; i <= n; i++) {
		cin >> x;
		num[x]++;
		maxx = max(maxx, x);
		ans = gcd(ans, x);
	}
	if (ans != 1) cout << "not coprime\n";
	else {
		for (i = 2; i <= maxx; i++) {
			for (j = i, res = 0; j <= maxx; j += i) res += num[j];
			if (res > 1) {
				cout << "setwise coprime";
				return 0;
			}
		}
		cout << "pairwise coprime\n";
	}
	return 0; 
}
