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
#include <cstdio>
#include <algorithm>
using namespace std;
int a[100005],pre[100005],post[100005];
int gcd(int a,int b)
{
 return b==0?a:gcd(b,a%b);
}
int main()
{
 int n,ans=1;
 scanf("%d",&n);
 for(int i=1;i<=n;i++)
  scanf("%d",&a[i]);
 pre[1]=a[1],post[n]=a[n];
 for(int i=1;i<=n;i++)
  pre[i]=gcd(pre[i-1],a[i]);
 for(int i=n-1;i;i--)
  post[i]=gcd(post[i+1],a[i]);
 for(int i=1;i<=n;i++)
  ans=max(ans,gcd(pre[i-1],post[i+1]));
 printf("%d\n",ans);
 return 0;
}