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
#import<bits/stdc++.h>
int i,m,n,t=2,a[100001];
int main()
  {
  for(scanf("%d",&n);i<n;)scanf("%d",a+i++);
  std::sort(a,a+n);
  for(m=a[1]+1;t>1;)
    {
    m--;
    for(i=t=0;t<2&i<n;i++)t+=a[i]%m>0;
    }
  printf("%d",m);
  }