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 = raw_input()
def gcd(a,b):
	if b == 0:
		return a
	return gcd(b,a%b)

def g(ais): return reduce(gcd, ais) == 1

def f(ais):
	seen = set()
	for ai in ais:
		factor =2
		oi = ai
		while(ai != 1 and factor * factor <= oi):
			if ai % factor == 0:
				if factor in seen:
					return False
				while(ai % factor == 0):
					ai /= factor
				seen.add(factor)
			factor +=1
		if ai != 1:
			if ai in seen: return False
			seen.add(ai) 
	return True

ais = map(int, raw_input().split())

if f(ais):
	print 'pairwise coprime'
elif g(ais):
	print 'setwise coprime'
else:
	print 'not coprime'