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 gcd(int a,int b){
  if(a>b)
    return gcd(b,a);
  if(a==0)
    return b;
  return gcd(b%a,a);
}
int main(){
  int n;
  cin>>n;
  vector<int> a(n);
  for(int i=0;i<n;i++)
    cin>>a.at(i);
  int gp=a.at(0);
  int g0=0;
  int p=0;
  for(int i=1;i<n;i++){
    if(gcd(gp,a.at(p))>gcd(gp,a.at(i))){
      gp=gcd(gp,a.at(p));
      p=i;
    }else
      gp=gcd(gp,a.at(i));
    g0=gcd(g0,a.at(i));
  }
  cout<<max(g0,gp)<<endl;
}