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;
int a[1000005];
bool v[1000005];

int main(){
    int n;
    cin >> n;
    bool pair = false;
    int num;
    for(int i = 0; i < n; ++i){
        cin >> num;
        ++a[num];
    }
    for(int i = 2; i <= 1000000; ++i)
        if(!v[i]){
            int t = 0;
            for(int j = 1; j * i <= 1000000; ++j){
                t += a[j * i];
                v[j * i] = true;
            }
            if(t == n){
                cout << "not coprime\n";
                return 0;
            }else if(t >= 2)
                pair = true;
        }

    if(pair)
        cout << "setwise coprime\n";
    else
        cout << "pairwise coprime\n";
    return 0;
}
