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=int(input())
l=[*map(int,input().split())]
f=lambda p: exit(print(['pairwise','setwise','not'][p]+' coprime'))
from math import *
g=l[0]
for x in l: g=gcd(g,x)
if g>1: f(2)
from collections import *
C=Counter()
b=0
for x in l:
  if x%2<1:
    if C[2]: f(1)
    C[2]=1
  while x%2<1: x//=2
  for i in range(3,int(x**0.5)+1,2):
    if x%i<1:
      if C[i]: f(1)
      C[i]=1
    while x%i<1: x//=i
    if x<2: break
  if x>1:
    if C[x]: f(1)
    C[x]=1
f(0)