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;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
int gcd(int a,int b){
   if(a==0) return b;
   else if(a<b){a^=b;b^=a;a^=b;}
   return a%b?gcd(b,a%b):b; 
}
int main() {
  int n,b=0,ans;
  cin>>n;
  int a[n],v[n+1];
  v[0]=0;
  rep(i,n)
  {
     cin>>a[i];
     v[i+1]=gcd(v[i],a[i]);
  }
  ans=v[n-1];
  for(int i=n-1;i>=1;i--){
      ans=max(ans,gcd(v[i-1],b=gcd(b,a[i])));
  }
  cout<<ans;
}