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;
  cin >> n;
  vector<int> a(n);
  for(int i = 0;i < n;i++)cin >> a[i];
  sort(a.begin(),a.end());
  int cnt;
  for(int i = a[1];i > 0;i--){
    cnt = 0;
    for(int j = 0;j < n;j++){
      if(a[j] % i != 0)++cnt;
      if(cnt == 2){
        break;
      }
    }
    if(cnt == 0||cnt == 1){
      cout << i << endl;
      break;
    }
    if(i == 1){
      cout << 1 << endl;
    }
  }
}