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 <iostream>
#include <string>
#include <algorithm>
#include <cmath>
using namespace std;

int main(){
  int n;
  cin >> n;
  int a[n];

  for(int i=0; i<n; i++) cin >> a[i];
  sort(a, a+n);

  int ans;
  for(int i=a[1]; i>=0; i--){
    int count = 0;
    for(int j=0; j<n; j++){
      if(a[j]%i != 0){
        count++;
        if(count == 2) break;
      }
    }
    if(count < 2){
      ans = i;
      break;
    }
  }
  cout << ans << endl;
  return 0;
}
