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 = [int(i) for i in input().split()]
maxA=max(A)
pn=list(range(maxA+1))
n=2
while n*n <= maxA:
  if n == pn[n]:
    for m in range(n, len(pn), n):
      if pn[m] == m:
        pn[m] = n
  n+=1

s=set()
for a in A:
  st = set()
  while a > 1:
    st.add(pn[a])
    a//=pn[a]
  if not s.isdisjoint(st):
    break
  s |= st
else:
  print("pairwise coprime")
  exit()

from math import gcd

n = gcd(A[0], A[1])
for a in A[2:]:
  n=gcd(n,a)
if n == 1:
  print("setwise coprime")
else:
  print("not coprime")
