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
from collections import defaultdict
from math import gcd

def solve():
    N = int(input())
    A = list(map(int, input().split()))
    all = 0
    for a in A:
        all = gcd(all, a)
    if all != 1:
        return "not coprime"

    M = 10 ** 6
    B = defaultdict(int)
    for a in A:
        B[a] += 1

    for i in range(2, M + 1):
        cnt = 0
        for j in range(i, M, i):
            cnt += B[j]
        if cnt > 1:
            return "setwise coprime"

    return "pairwise coprime"

print(solve())
