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=list(map(int,input().split()))
l=[0]*(10**6+100)
x=0
for m in a:
  l[m]+=1

j=2
#print(l)


while j <10**6+1:
  c=0
  k=1
  while j*k<=10**6+1 :
    if l[j*k]>0:
      c+=l[j*k]
    k+=1

  if c==n:
    print("not coprime")
    exit()
  elif c>1:
    x=1
  j+=1 
  
if x==1:
  print("setwise coprime")
else:
  print("pairwise coprime")
  
    
