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
M=10**6+1
f=lambda p: exit(print(['pairwise','setwise','not'][p]+' coprime'))
n=int(input())
l=[*map(int,input().split())]
g=0
from math import *
for x in l:
  g=gcd(g,x)
if g>1: f(2)
def sieve(x):
  p=[]
  s=[0]*x
  for i in range(2,x):
    if s[i]<1:
      p+=[i]
      for j in range(i,x,i): s[j]=i
  return s
s=sieve(M)
C=[0]*M
for x in l:
  t=set()
  while x>1:
    t.add(s[x])
    x//=s[x]
  for y in t:
    if C[y]: f(1)
    C[y]=1
f(0)