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