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 math import gcd
n = int(input())
a = list(map(int, input().split()))
max_a = max(a)
cnt_a = [0] * (max_a + 1)
for ai in a:
  cnt_a[ai] += 1
ans = 'pairwise'
for i in range(2, max_a + 1):
  cnt = 0
  for j in range(i, max_a + 1, i):
    cnt += cnt_a[j]
  if cnt > 1:
    ans = 'setwise'
g = 0
for ai in a:
  g = gcd(g, ai)

if ans == 'pairwise':
  print(ans, 'coprime')
elif ans == 'setwise' and g == 1:
  print(ans, 'coprime')
else:
  print('not coprime')
