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){
      	final int A = 1000005;
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        //与えられる整数を格納する配列
      	int a[] = new int [n];
        //与えられた整数iの個数を数える配列cを用意し、c[i]に格納する
        int c[] = new int [A];
        int b;
        String ans = "pairwise coprime";
        for(int i = 0; i < A; i++){
            c[i] = 0;
        }
        for(int i = 0; i < n; i++){
            b = sc.nextInt();
            c[b] += 1;
        }

        //配列cを使って公約数を調べる。
        //iの倍数である数がいくつあるかを数える。cnt==n であればnot coprime
        //n > cnt > 1ならばsetwise coprime
        for(int i = 2; i < A; i++){
            int cnt = 0;
            for(int j = i; j < A; j += i){
                cnt += c[j];
            }
            if(cnt == n){
                ans = "not coprime";
                break;
            }else if(cnt > 1){
                ans = "setwise coprime";
            }
        }
        
        System.out.println(ans);
    }
}
