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(b==0)return a;
  else return gcd(b,a%b);
}
 
int main() {
  int n,a[114514],l[114514],r[114514];
  cin >> n;
  for(int i=0;i<n;i++)cin >> a[i];
  l[0]=0;
  r[0]=0;
  for(int i=0;i<n;i++){
    l[i+1]=gcd(l[i],a[i]);
    r[i+1]=gcd(r[i],a[n-1-i]);
  }
  int res=0;
  for(int i=0;i<n;i++){
    if(res<gcd(l[i],r[n-1-i]))res=gcd(l[i],r[n-1-i]);
  }
  cout << res << endl;
}