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
k=10**6+1
def judge(n,a):
  c=[0]*k
  for x in a:
    c[x]+=1 #対応する数の個数を記録
  t=any(sum(c[i::i])>1 for i in range(2,k)) #自身を約数に持つ数が2つ以上与えられたリストに存在するような数が一つでもあるかどうか
  t+=reduce(gcd,a)>1 #全体について1以外の公約数があれば1加える
  return ['pairwise','setwise','not'][t]+' coprime' #全体に公約数があればt=2,全体の公約数が1で公約数持つペアがあればt=1
n=int(input())
a=list(map(int,input().split()))
print(judge(n,a))
