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 sys import stdin, stdout
from math import gcd
N=10**6+2
n = int(stdin.readline())
a = list(map(int, stdin.readline().split()))
mp=[0]*N;not_pairwise=1
for v in a:
    mp[v]+=1
for i in range(2,N):
    if sum(mp[i::i])>1:
        not_pairwise=0
        break
g = a[0]
for v in a:
    g = gcd(g, v)
if not_pairwise:
    print('pairwise coprime')
elif g == 1:
    print('setwise coprime')
else:
    print('not coprime')