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;
typedef long long ll;
#define pb push_back
#define fr(i,n) for(int i=0;i<n;i++)
#define ifr(i,n) for(int i=n-1;i>=0;i--)


int main() {
  int n;
  cin >>n;
  int a[n];
  int ans =0;
  int memo = 0;
  int x;
  fr(i,n){
    cin >>a[i];
  }
  sort(a, a+n);
  for(x=a[1];x>=0;x--){
    memo = 0;
    fr(j,n){
      if(a[j]%x!=0){
        memo+=1;
      }
    }
    if(memo <=1)break;
  }
  cout << x << endl;
}