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

N = int(input())
a = list(map(int,input().split()))
m = max(a)
c = [0] * (m+1)

for i in a:
  c[i] += 1

pairwise = True
for i in range(2, m+1, 1):
  cnt = 0
  for j in range(i, m+1, i):
    cnt += c[j]
    if cnt > 1:
      pairwise = False
      break
if pairwise:
  print("pairwise coprime")
  exit()

g = 0
for i in range(N):
  g = math.gcd(g, a[i])
if g == 1:
  print("setwise coprime")
  exit()

print("not coprime")