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>
#include <math.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  for(int i = 0; i < N; i++) cin >> A.at(i);
  sort(A.begin(), A.end());

  int count;
  int GCD = 1;
  for(int i = max(A.at(0), A.at(1)); i > 1 ; i--){
    count = 0;
    for(int x : A){
      if(x % i != 0) count++;
    }
    if(count <= 1){
      GCD = i;
      break;
    }
  }
  cout << GCD << endl;
}
