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;

int main() {
  int n,ans,count=0;
  cin>>n;
  long long a[n];
  for(int i=0;i<n;i++){
    long long k;
    cin>>k;
    a[i]=k;
  }
  sort(a,a+n);
  for(int i=a[1];i>0;i--){
    if(a[1]%i==0||a[0]%i==0){
      for(int j=0;j<n;j++){
        if(a[j]%i==0)count++;
      }
    }
    if(count>n-2){
      ans=i;
      break;
    }
    else count=0;
  }
  cout<<ans<<endl;
}
