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;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
typedef long long ll;

int main(void){

  int n,i,ans=0,maxa=0;
  cin>>n;
  vector<int> a(n);
  
  rep(i,n)cin>>a[i];
  sort(a.begin(),a.end());
  int c;
  rep(i,a[1]){
    c=0;
    rep(j,n){
      ans = a[1]-i;
      if(a.at(j)%ans!=0) ++c;
      if(c>2)break;
    }
    if(c<=1){cout<<ans;return 0;}
  }
  
}