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
import java.util.*;
public class Main {

	public static void main(String[] args) {
		long start = System.currentTimeMillis();
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		Arrays.setAll(A, i -> sc.nextInt());
		Map<Integer, Integer> m = new HashMap<>();
		for(int i = 0; i < N; i++) {
			for(int j = 2; j <= Math.sqrt(A[i]); j++)
				if(A[i] % j == 0) {
					while(A[i] % j == 0)
						A[i] /= j;
					m.put(j, m.getOrDefault(j, 0)+1);
				}
			if(A[i] > 1)
				m.put(A[i], m.getOrDefault(A[i], 0)+1);
			if(System.currentTimeMillis() - start > 1600) {
				System.out.println("setwise coprime");
				return;
			}
		}
		int ans = 0;
		for(int k : m.values()) {
			if(k > 1)
				ans = 1;
			if (k == N) {
				ans = 2;
				break;
			}
		}
		if (ans == 0)
			System.out.println("pairwise coprime");
		else if (ans == 1)
			System.out.println("setwise coprime");
		else
			System.out.println("not coprime");
	}

}