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(x) for x in input().split()]

u=10**6+1
C=[0]*u
D=[0]*2+[1]*(u-2)

def gcd(a,b):
   while a%b:
     a,b=b,a%b
   return b

n=4
while n<u:
  D[n]=0
  n+=2
i=3
while i*i<u:
  if D[i]:
    n=i*2
    while n<u:
      D[n]=0
      n+=i
  i+=2

for a in A:
  C[a]+=1
for i in [x for x in range(2,u) if D[x]==1]:
  if sum(C[i::i])>1:
    break
else:
  print('pairwise coprime')
  exit()

c=A[0]
for a in A:
  c=gcd(c,a)
  if c==1:
    break
else:
  print('not coprime')
  exit()

print('setwise coprime')
