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 math import gcd 

n = int(input())
maxA = 10**6+5
A = list(map(int, input().split()))
c = [0]*maxA
for a in A:
    c[a] += 1

for i in range(2, maxA):
    cnt = 0
    for j in range(i, maxA, i):
        cnt += c[j]
    if cnt >= 2:
        break
else:
    print('pairwise coprime')
    exit()

g = 0
for a in A:
    g = gcd(g, a)
if g == 1:
    print('setwise coprime')
else:
    print('not coprime')