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
from fractions import gcd

n = int(input())
a = list(map(int, input().split()))

left = [0]
right = [0]

for i in range(n):
    left.append(gcd(left[i], a[i]))
    right.append(gcd(right[i], a[n - i - 1]))

ans = 0
for i in range(n):
    ans = max(ans, gcd(left[i], right[n - i - 1]))

print(ans)