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<bits/stdc++.h>
using namespace std;
const int N=100010;
int p[N],s[N],a[N];
int gcd(int x,int y)
{
  if(y==0) return x;
  return gcd(y,x%y);
}
int main()
{
  int n,ans=0;
  cin>>n;
  p[0]=s[n+1]=0;
  for(int i=1;i<=n;i++)
  {
    cin>>a[i];
    p[i]=gcd(p[i-1],a[i]);
  }
  for(int i=n;i>=1;i--) s[i]=gcd(s[i+1],a[i]);
  for(int i=1;i<=n;i++) ans=max(ans,gcd(p[i-1],s[i+1]));
  cout<<ans<<endl;
  return 0;
}
