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.*;
import java.io.*;
public class Main {

	static Scanner inp= new Scanner(System.in);
	static PrintWriter out= new PrintWriter(System.out);
	public static void main(String args[]) {		    	
	   	Main g=new Main();
	   	g.main();
	   	out.close();
	}

	
	
	//Main
	void main() {
		
		int n=inp.nextInt();
		int a[]=new int[n];
		int N=(int)1e6+1;
		int sp[]=new int[N];
		sp[1]=1;
		for(int i=2;i<N;i++) {
			if(sp[i]==0) {
				for(int j=i;j<N;j+=i) {
					if(sp[j]==0) sp[j]=i;
				}
			}
		}
		for(int i=0;i<n;i++) {
			a[i]=inp.nextInt();
		}
		//for(int i=0;i<=6;i++) System.out.println(sp[i]);
		int usedIndex[]=new int[N];
		Arrays.fill(usedIndex, -1);
		boolean pairCo=true;
		loop:
		for(int i=0;i<n;i++) {
			int x=a[i];
			while(x>1) {
				if(usedIndex[sp[x]]!=-1 && usedIndex[sp[x]]!=i) {
					pairCo=false;
					break loop;
				}
				usedIndex[sp[x]]=i;
				x/=sp[x];
			}
		}
		if(pairCo) {
			System.out.println("pairwise coprime");
		}else {
			int x=a[0];
			for(int i=1;i<n;i++) {
				x=gcd(x,a[i]);
			}
			System.out.println(x==1?"setwise coprime":"not coprime");
		}
	}
    
    static int gcd(int a, int b) {
    	return b==0?a:gcd(b,a%b);
    }
		
}
