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<cmath>
#include<algorithm>
using namespace std;
int n,a[1000005],ans=1;
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    sort(a+1,a+n+1);
    for(int i=a[2];i>=2;i--)
    {
        int t=0;
        for(int j=1;j<=n;j++)
        {
            if(a[j]%i!=0) t++;
            if(t>=2) break;
        }
        if(t<=1)
        {
            ans=i;
            break;
        }
    }
    printf("%d",ans);
    return 0;
}