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, = map(int, input().split())
m = max(2, max(A))
P = {p: True for p in range(2, m + 1)}
for i in range(2, m + 1):
    for j in range(2 * i, m + 1, i):
        P[j] = False
Pmap = {p: 0 for p in P if P[p]}
Amap = {a: 0 for a in range(1, m + 1)}
for a in A:
    Amap[a] += 1
for p in Pmap:
    for a in range(p, m + 1, p):
        Pmap[p] += Amap[a]
s = max(Pmap.values())
if s < 2:
    print('pairwise coprime')
elif s < n:
    print('setwise coprime')
else:
    print('not coprime')
