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[] $){
		var s=new Scanner(System.in);
		var n=s.nextInt();
		var a=new int[n];
		Arrays.setAll(a,i->s.nextInt());

		var p=new int[1000000];

		var pairwise=true;

		for(int v: a){
			for(int i=2;i<=v;++i){
				if((long)i*i>v){
					if(v>1&&++p[v] >= 2)
						pairwise=false;
					break;
				}
				if(v%i==0){
					if(++p[i] >= 2)
						pairwise=false;
					while(v%i==0)
						v/=i;
				}
			}
		}

		if(pairwise)
			System.out.println("pairwise coprime");
		else if(!Arrays.stream(p).anyMatch(i->i==n))
			System.out.println("setwise coprime");
		else
			System.out.println("not coprime");

	}
}
