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;

const int m = 1000000;
int n, h[m + 5];
bool f, g;

int main() {
    scanf("%d", &n);
    for (int i = 1, t; i <= n; i++)
        scanf("%d", &t), h[t]++;
    f = g = true;
    for (int i = 2; i <= m; i++) {
        int tot = 0;
        for (int j = i; j <= m; j += i)
            tot += h[j];
        if (tot > 1)
            f = false;
        if (tot == n)
            g = false;
    }
    if (f)
        printf("pairwise coprime");
    else if (g)
        printf("setwise coprime");
    else
        printf("not coprime");
    return 0;
}