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,a=int(input()),list(map(int,input().split()))
g=0
from math import gcd
for i in a:g=gcd(i,g)
if g!=1:print("not coprime")
else:
    from collections import defaultdict
    memo=defaultdict(int)
    for i in a:
        for p in range(2,int(i**.5)+1):
            if i%p==0:
                while i%p==0:i//=p
                if memo[p]:
                    print("setwise coprime");exit()
                memo[p]+=1
        if i!=1:
            if memo[i]:print("setwise coprime");exit()
            memo[i]+=1
    print("pairwise coprime")