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>
#define rep(i, n) for(int i = 0; i < (n); i++)
using namespace std;
using ll = long long;
using pii = pair<int, int>;

const int MAX = 1000005;

int gcd(int a, int b) {
	if (b == 0) return a;
	else return gcd(b, a % b);
}

int main() {
	int n;
	cin >> n;
	vector<int> a(n);
	rep(i, n) cin >> a[i];
	vector<int> s(MAX);
	rep(i, n) s[a[i]]++;
	bool ok = true;
	for (int i = 2; i < MAX; i++) {
		int cnt = 0;
		for (int j = i; j < MAX; j += i) cnt += s[j];
		if (cnt > 1) ok = false;
	}
	if (ok) {
		cout << "pairwise coprime" << endl;
		return 0;
	}
	int g = 0;
	rep(i, n) g = gcd(g, a[i]);
	if (g == 1) cout << "setwise coprime" << endl;
	else cout << "not coprime" << endl;
	return 0;
}