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())
Alist = [0]+list(map(int, input().split()))+[0]
Rlist = [0]*(N+2)
Llist = [0]*(N+1)
for i in range(N):
    Llist[i+1] = gcd(Llist[i], Alist[i])
    Rlist[N-i] = gcd(Rlist[N-i+1], Alist[N-i+1])
print(max([gcd(Rlist[i], Llist[i]) for i in range(1,N+1)]))
