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 <iostream>
using namespace std;

int gcd(int a, int b) {return b ? gcd(b, a % b) : a;}

int n, cnt[1000001];
bool flag = 0;

int main()
{
	int res = 0;
	cin >> n;
	for (int i = 0; i < n; i++) {int x; cin >> x; cnt[x]++; res = gcd(res, x);}
	for (int i = 2; i <= 1000000; i++)
	{
		int c = 0;
		for (int j = i; j <= 1000000; j += i) {c += cnt[j];}
		if (c > 1) {flag = 1; break;}
	}
	if (flag)
	{
		if (res == 1) {cout << "setwise coprime\n";}
		else {cout << "not coprime\n";}
	}
	else {cout << "pairwise coprime\n";}
	return 0;
}