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
from fractions import gcd

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

A = max(As)
lst = [0]*(A+1)
rlt = [0]*(A+1)

for i in range(2, A+1):
  if lst[i] > 0:
    continue
  j = 1
  while i*j <= A:
    if lst[i*j] == 0:
      lst[i*j] = i
    j += 1
  if j == 1:
    break
    
for a in As:
  tmp = -1
  while a > 1:
    if tmp != lst[a]:
      rlt[lst[a]] += 1
      tmp = lst[a]
    a //= lst[a]

r = max(rlt) 

if r < 2:
  print('pairwise coprime')
elif r < N:
  print('setwise coprime')
else:
  print('not coprime')