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(a, b):
    if a < b:
        return gcd(b, a)
    while b > 0:
        a, b = b, a % b
    return a

n = int(input())
a_list = list(map(int, input().split()))

checker = [0] * (10 ** 6 + 1)
x = a_list[0]
for a in a_list:
    x = gcd(x, a)
    checker[a] += 1

if all(sum(checker[d::d]) <= 1 for d in range(2, 10 ** 6 + 1)):
    print("pairwise coprime")
elif x == 1:
    print("setwise coprime")
else:
    print("not coprime")
    


