There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Examples

Input

3
7 6 8


Output

2


Input

3
12 15 18


Output

6


Input

2
1000000000 1000000000


Output

1000000000
def gcd(x,y):
    while y != 0:
        x,y = y,x%y
    return x
n = int(input())
a = list(map(int,input().split()))

L,R = [0],[0]
for i in range(1,n+1): #L[i]は左i個,R[i]は右i個
    L.append(gcd(L[-1],a[i-1]))
    R.append(gcd(R[-1],a[n-i]))
print(max(gcd(L[i],R[n-i-1]) for i in range(n)))