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

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

v = 0
for a in A: v = gcd(a, v)
if v > 1:
	print('not coprime')
	raise SystemExit


V = set()
for v in A:
	for i in range(2, v+1):
		if i * i > v: break
		if v % i == 0:
			if v in V:
				print('setwise coprime')
				raise SystemExit

			V.add(v)
			while v % i == 0: v //= i
	if v != 1:
		if v in V:
			print('setwise coprime')
			raise SystemExit

		V.add(v)

print('pairwise coprime')
