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) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        int g = gcd(a[0], a[1]);
        for (int i = 2; i < n; i++) {
            g = gcd(g, a[i]);
        }
        Set<Integer> set = new HashSet<>();
        boolean pc = true;
        for (int i = 0; i < n; i++) {
            if(!pc) break;
            int tmp = a[i];
            for (int j = 2; j < Math.sqrt(a[i]); j++) {
                boolean hasj = false;
                while(tmp % j == 0){
                    hasj = true;
                    tmp /= j;
                }
                if(hasj && set.contains(j)){
                    pc = false; break;
                }
                if(hasj) set.add(j);
                if(tmp == 1) break;
            }
            if(tmp != 1){
                if(set.contains(tmp)) pc = false;
                else set.add(tmp);
            }
        }
        if(pc)  System.out.println("pairwise coprime");
        else if(g == 1) System.out.println("setwise coprime");
        else System.out.println("not coprime");
        sc.close();

    }

    public static int gcd(int a, int b) {
        if (a < b)
            return gcd(b, a);
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }


}
