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 factorize(x):
    f = set()
    if x%2==0: f.add(2)
    while x%2==0: x//=2
    
    p = 3
    while x>=p*p:
        if x%p==0: f.add(p)
        while x%p==0: x//=p
        p+=2
    if x>1: f.add(x)
    return f

N = int(input())
A = list(map(int, input().split()))

F = [0]*(10**6+5)

for a in A:
    for f in factorize(a):
        F[f] += 1

m = max(F)
if m<=1:
    print('pairwise coprime')
elif m<N:
    print('setwise coprime')
else:
    print('not coprime')
