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
from math import gcd
from functools import reduce
from collections import defaultdict
n=int(input())
a=list(map(int,input().split()))

if reduce(gcd,a)!=1:
  print("not coprime")
  exit()

def primes(x):
  ret=[]
  for i in range(1,int(x**0.5)+1):
    if x%i==0:
      ret.append(i)
      if x//i!=i:
        ret.append(x//i)
  ret.sort()
  return ret[1:]
      
s=set()
for q in a:
  p=primes(q)
  for j in p:
    if j in s:
      print("setwise coprime")
      exit()
    s.add(j)
print("pairwise coprime")
