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
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;


int gcd(int x,int y){
	if(!y)return x;
	return gcd(y,x%y);
}

int N,A[1000000];
bool K[1000001];

int main(){
	cin>>N;
	for(int i=0;i<N;i++){
		cin>>A[i];
	}
	int t=0;
	for(int i=0;i<N;i++){
		t=gcd(t,A[i]);
	}
	if(t==1){
		for(int i=0;i<N;i++){
			for(int j=2;j*j<=A[i];j++){
				if(A[i]%j==0){
					if(K[j]){
						puts("setwise coprime");
						return 0;
					}
					K[j]=true;
					while(A[i]%j==0){
						A[i]/=j;
					}
				}
			}
			if(A[i]!=1){
				if(K[A[i]]){
					puts("setwise coprime");
					return 0;
				}
				K[A[i]]=true;
			}
		}
		puts("pairwise coprime");
	}
	else{
		puts("not coprime");
	}
}
