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
def main():
    from math import gcd
    n, *a = map(int, open(0).read().split())
    m = max(a)

    c = [0] * (m + 1)
    g = a[0]
    for i in a:
        g = gcd(g, i)
        c[i] = 1

    if g > 1:
        pre = "not"
    else:
        for i in range(2, 10 ** 6 + 1):
            if sum(c[i::i]) > 1:
                pre = "setwise"
                break
        else:
            pre = "pairwise"

    print(pre + " coprime")


if __name__ == '__main__':
    main()
