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
import sys
input=sys.stdin.readline

def gcd(a,b):
  if b==0:
    return a
  else:
    return gcd(b,a%b)
def calc():
  n=int(input())
  arr=list(map(int,input().split()))
  g=arr[0]
  cnt=[0]*(10**6+1)
  for val in arr:
    g=gcd(g,val)
    cnt[val]+=1
  for i in range(2,10**6+1):
    tmp=0
    for j in range(i,10**6+1,i):
      tmp+=cnt[j]
    if tmp>=2:
      break
  if i==10**6:
    print('pairwise coprime')
  elif g==1:
    print('setwise coprime')
  else:
    print('not coprime')
calc()