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()))
m = [0]*n

l, r = [0]*n, [0]*n
for i in range(1, n):
    l[i] = gcd(a[i-1], l[i-1])
    r[n-1-i] = gcd(r[n-i], a[n-i])

ans = 1
for a, b in zip(l, r):
    x = gcd(a, b)
    if ans < x:
        ans = x

print(ans)