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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = Integer.parseInt(scan.next());
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(scan.next());
        }
        scan.close();

        boolean isPairwise = true;
        Set<Integer> set = new HashSet<Integer>();
        for (int i = 0; i < n; i++) {
            int curA = a[i];
            for (int j = 2; j <= Math.sqrt(curA); j++) {
                if (curA % j == 0) {
                    if (set.contains(j)) {
                        isPairwise = false;
                        break;
                    }

                    set.add(j);
                    while (curA % j == 0) {
                        curA /= j;
                    }
                }
            }

            if (curA >= 2) {
                if (set.contains(curA)) {
                    isPairwise = false;
                } else {
                    set.add(curA);
                }
            }

            if (!isPairwise) {
                break;
            }
        }

        if (isPairwise) {
            System.out.println("pairwise coprime");
            return;
        }

        int gcd = a[0];
        for (int i = 1; i < n; i++) {
            gcd = calcGcd(gcd, a[i]);
        }

        if (gcd == 1) {
            System.out.println("setwise coprime");
        } else {
            System.out.println("not coprime");
        }

    }

    private static int calcGcd(int a, int b) {
        if (a % b == 0) {
            return b;
        } else {
            return calcGcd(b, a % b);
        }
    }
}
