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,rieki,answer;
	cin >> n;
  vector<int> vec(n);
  for(int i=0;i<n;i++){
    cin>>vec.at(i);
  }
  sort(vec.begin(), vec.end());
for(int k=vec.at(1);0<k;k--){
  int count=0;
  for(int l=0;l<n;l++){
  if(vec.at(l)%k==0){
    continue;
  }
  else{
    count+=1;
  }
}
if(count==0 || count==1){
  answer =k;
  break;
}
}
cout<<answer<<endl;
}
