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;
  vector<int> A;
  
  cin>>N;
  for(int i=0;i<N;i++){
    int x;
    cin>>x;
    A.push_back(x);
  }
  
  sort(A.begin(),A.end());
  int M = A.at(1);
  
  int answer;
  
  for(int i=M;i>0;i--){
    int x=0;
    for(int j=0;j<N;j++){
      if (A.at(j)%i!=0) x++;
      if (x>1) break;
    }
    if (x<=1) {
      answer = i;
      break;
    }
  }
  
  cout<<answer<<endl;
}