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, raw_input().split()))

forward = []
backward = [0 for x in range(n)]

if n == 2:
    print(max(a[0], a[1]))
    exit(0)

for i in range(n):
    if i == 0:
        forward.append(a[i])
    else:
        forward.append(gcd(forward[i - 1], a[i]))


for i in range(n - 1, -1, -1):
    if i == n - 1:
        backward[i] = a[i]
    else:
        backward[i] = gcd(backward[i + 1], a[i])


ans = 1

for i in range(n):
    if i == 0:
        ans = max(ans, backward[1])
    elif i == n - 1:
        ans = max(ans, forward[n - 2])
    else:
        ans = max(ans, gcd(forward[i - 1], backward[i + 1]))

print(ans)
