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 gcd_all(A):
    from math import gcd
    g = 0
    for a in A: g = gcd(g, a)
    return g

def is_pairwise():
    C = [0] * (10**6 + 1)
    max_a = 0
    for a in A:
        C[a] += 1
        max_a = max(max_a, a)
    if sum(C[2::2]) > 1: return False
    for i in range(3, max_a + 1, 2):
        if sum(C[i::i]) > 1: return False
    return True

def solve():
    if is_pairwise(): return 0
    if gcd_all(A) == 1: return 1
    return 2

n = int(input())
A = [*map(int, input().split())]
print(['pairwise','setwise','not'][solve()], 'coprime')
