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=list(map(int,input().split()))

s=set()
f=1
for x in a:
	if f==0:
		break
	if x>1:
		r=int(x**0.5+1e-8)+1
		for i in range(2,r):
			if x%i==0:
				while x%i==0:
					x//=i
				if i in s:
					f=0
					break
				else:
					s.add(i)
		if x>1:
			if x in s:
				f=0
				break
			else:
				s.add(x)

if f:
	print("pairwise coprime")
	exit()
p=a[0]
from math import gcd
for x in a:
	p=gcd(p,x)
if p==1:
	print("setwise coprime")
else:
	print("not coprime")

