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 <algorithm>
#include <string>
#include <vector>

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);
 // cout << A[1];
  int i = A[1];


  for (; i > 0; i--){
    int count = 0;
    for ( int j = 0; j < N; j++){
      if (A[j] % i == 0) count++;
    }
    if (count >= N-1) {
      cout << i;
      break;
    }
  
  }

}
