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<iostream>
using namespace std;
int gcd(int a,int b){return b?gcd(b,a%b):a;}
int N;
int cnt[1<<20];
int all=0;
bool isp[1<<20];
int main(){
	cin>>N;
	for(int i=0;i<N;i++){
		int A;cin>>A;
		cnt[A]++;
		all=gcd(all,A);
	}
	bool ok=true;
	for(int i=2;i<1<<20;i++){
		int sum=0;
		for(int j=i;j<1<<20;j+=i)
        	sum+=cnt[j];
		if(sum>1)
        	ok=false;
	}
	cout<<(ok?"pairwise coprime":all==1?"setwise coprime":"not coprime")<<endl;
}