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())
import copy
a= [int(x) for x in input().split()]
MAX_A = 10 ** 6 + 1
histogram = [0] * MAX_A
for x in a:
  histogram[int(x)] += 1
for divider in range(2, MAX_A):
  count = 0
  for counted in histogram[divider::divider]:
    count += counted
  if count > 1:
    break
else:
  print('pairwise coprime')
  exit()
from math import gcd
g=gcd(a[0],a[1])
if n==2:
  print('setwise coprime' if g==1 else 'not coprime')
  exit()
for i in range(2,n):
  g=gcd(g,a[i])
if g==1:
  print('setwise coprime')
else:
  print('not coprime')
