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>
 
 
using namespace std;
 
template<class T> inline int gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
 
 
 
int main(){
 
int n;
  cin >> n;
  int a[n];
 
  for(int i=0;i<n;i++){
   cin >> a[i];
  }
    
  int l[n+1],r[n+1];
  
  l[0]=0;
  r[n]=0;
  
  for(int i=0; i<n;i++){
   l[i+1]=gcd(l[i],a[i]);
   r[n-i-1]=gcd(r[n-i],a[n-i-1]);
  }
  
 
  
  int m=0;
  for(int i=0;i<n;i++){
  m=max(m,gcd(l[i],r[i+1]));
  }
  
  
 cout << m << endl;
 
 
}