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;
  return gcd(b,a%b);
}
int main(){
  int n;
  cin>>n;
  vector<int> a(n),l,r;
  for(auto& c:a)cin>>c;
  l=r=a;
  for(int i=1;i<n;++i){
    l[i]=gcd(l[i],l[i-1]);
    r[n-1-i]=gcd(r[n-1-i],r[n-i]);
  }
  int res=1;
  for(int i=0;i<n;++i)res=max(res,gcd(i?l[i-1]:0,i+1<n?r[i+1]:0));
  cout<<res;
  return 0;
}