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