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())
a = list(map(int,input().split()))
M = max(a)+1
if M == 2:
    print("pairwise coprime")
    exit()
count = [0]*(M)

for i in range(2,M):
    if count[i] == 0:
        for j in range(i,M,i):
            if count[j] == 0:
                count[j] = i
check = [0]*(M)
for i in a:
    x = i
    while x > 1:
        check[count[x]] += 1
        y = count[x]
        while x%y == 0:
            x //= y
ans = max(check)
if ans == 1:
    print("pairwise coprime")
elif ans == n:
    print("not coprime")
else:
    print("setwise coprime")