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

read_ints = lambda : map(int, raw_input().strip().split())

n = input()
a = read_ints()

pre = [0] * (n + 1)
for i in xrange(1, n + 1):
    pre[i] = gcd(pre[i - 1], a[i - 1])

suf = [0] * (n + 1)
suf[n - 1] = a[n - 1]
for i in xrange(n - 2, -1, -1):
    suf[i] = gcd(suf[i + 1], a[i])

ans = pre[n]
for i in xrange(n):
    g1 = pre[i]
    g2 = suf[i + 1]
    g = gcd(g1, g2)
    ans = max(ans, g)

print ans