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
import sys
n = int(input())
a = list(map(int, input().split()))

ga = a[0]
for i in range(n):
  ga = math.gcd(ga, a[i])

if ga != 1:
  print("not coprime")
  sys.exit()

m = 1000000
b = [0]*(m+1)

for i in range(2, m):
  if b[i] != 0:
    continue
  j = 1
  while True:
    t = i * j
    if t > m:
      break
    if b[t] == 0:
      b[t] = i
    j += 1

d = {}
for i in a:
  p = i
  while p != 1:
    if p in d:
      print("setwise coprime")
      sys.exit()
    d[p] = 1
    p = int(p/b[p])
print("pairwise coprime")
