p02574 AtCoder Beginner Contest 177 - Coprime
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
```python
N = int(input())
A = list(map(int,input().split()))

A = sorted(A,reverse = True)
prime = [0] * (10**6+1)
eratos = [True] * (A[0] + 1)
D = [0] * (A[0]+1)
D[1] = 1
for i in range(2,A[0] + 1):
  if not eratos[i]:
    continue
  else:
    for j in range(i,A[0] + 1,i):
      if not D[j]:
        D[j] = i
      if j!=i:
      	eratos[j] = False
  
for a in A:
  while a!=1:
    x = D[a]
    while a%x==0:
      a//=x
    prime[x] += 1

if max(prime)<=1:
  print('pairwise coprime')
  
elif max(prime)!=N:
  print('setwise coprime')
else:
  print('not coprime')
```