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())
as_ = list(map(int, input().split()))

gcd_all = as_.pop()
set_ = {as_[0]}
for a in as_:
    set_ = set(gcd(s, a) for s in set_)
    set_.add(gcd_all)
    gcd_all = gcd(gcd_all, a)

print(max(set_))
