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
n = int(input())
a = list(map(int, input().split()))
li = [0] * 1100000
is_prime = [True] * 1100000
is_prime[0] = is_prime[1] = False
for i in a:
    li[i] += 1
is_pairwise = True
for i in range(2, 1100000):
    if is_prime[i]:
        cnt = 0
        for j in range(i, 1100000, i):
            is_prime[j] = False
            cnt += li[j]
        if cnt == n:
            print("not coprime")
            exit()
        if cnt > 1:
            is_pairwise = False
if is_pairwise:
    print("pairwise coprime")
else:
    print("setwise coprime")