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()]
ma=max(a)
memo=[0]*ma

def gcd(a,b):#最大公約数
  while b!=0:
    a,b=b,a%b
  return a

for i in a:
  memo[i-1]+=1

pair=True
for i in range(2,ma+1):
  cnt=0
  for j in range(i,ma+1,i):
    if 0<memo[j-1]:
      cnt+=1
  if 1<cnt:
    pair=False


g=a[0]
for i in range(1,n):
  g=gcd(g,a[i])

if pair == False and g==1:
  print("setwise coprime")
elif pair == True and g==1:
  print("pairwise coprime")
else:
  print("not coprime")
    