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;
#define LL long long

int main(){
	// sengen
	int n;
	// nyuryoku
	cin >> n;
	int a[n];
	int b[1000001] = {};
	int count = 0;
	for(int i=0;i<n;i++){
		cin >> a[i];
		b[a[i]]++;
	}
	int c = 1;
	// keisan
	int ans = 1;
	for(int i=2;i<=1000000;i++){
		int tmp = 0;
		for(int j=1;i*j<=1000000;j++){
			tmp += b[i*j];
		}
		if(tmp > 1){
			c = 0;
		}
		ans = max(ans,tmp);
	}
	if(c){
		cout << "pairwise coprime" << endl;
	}else if(ans == n){
		cout << "not coprime" << endl;
	}else{
		cout << "setwise coprime" << endl;
	}
	// syutsuryoku
}