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()))
 
flg = 0
l = [0]*(max(A)+1)
for i in A:
  l[i] += 1
a = gcd(A[0],A[1])
for i in range(2,N):
  a = gcd(a,A[i])
for i in range(2,max(A)+1):
  if sum(l[i::i]) > 1:
    flg = 1
    break



if a == 1 and flg == 0:
  print("pairwise coprime ")
elif a == 1 and flg == 1:
  print("setwise coprime")
else:
  print("not coprime")
