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
if True:
    N = int(input())
    As = list(map(int, input().split()))

    maxA = 10**6 + 6
    c = [0] * (maxA+1)
    for A in As:
        c[A] += 1
    isPrime = True
    cnt = 0
    for i in range(2, maxA+1):
        cnt = sum(c[i::i])
        if cnt == N:
            # Asはすべてiの約数
            print("not coprime")
            break
        if cnt >= 2:
            isPrime = False
        
    else:
        if isPrime:
            print("pairwise coprime")
        else:
            print("setwise coprime")



