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;

int main() {
	int N;
	cin >> N;
	vector<int> A(N);
	for (int i = 0; i < N; i++) cin >> A[i];
	map<int, int> P;
	for (int i = 0; i < N; i++) {
		for (int j = 2; j * j <= A[i]; j++) {
			if (A[i] % j == 0) {
				P[j]++;
				while (A[i] % j == 0) {
					A[i] /= j;
				}
			}
		}
		if (A[i] != 1) P[A[i]]++;
	}
	int MAX = 0;
	for (auto it = P.begin(); it != P.end(); it++) {
		MAX = max(MAX, it->second);
	}
	if (MAX <= 1) cout << "pairwise coprime" << endl;
	else if (MAX == N) cout << "not coprime" << endl;
	else cout << "setwise coprime" << endl;
}