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 math as mt
I=lambda:list(map(int,input().split()))
mod=10**9
n,=I()
l=I()
x=0
y=0
temp=l[0]
for i in range(1,n):
	temp=mt.gcd(temp,l[i])
N=10**6+3
ss=[0]*(N)
ss[0]=1
for i in range(2,N):
	if ss[i]==0:
		ss[i]=i
		for j in range(2*i,N,i):
			ss[j]=i
if temp!=1:
	print("not coprime")
else:
	pos=1
	visi=[0]*N
	for i in range(n):
		now=l[i]
		while now>1:
			te=ss[now]
			if visi[te]:
				pos=0
				break
			while now%te==0:
				now//=te
			visi[te]=1
		if not pos:
			break
	if pos:
		print("pairwise coprime")
	else:
		print("setwise coprime")
