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 x,int y){
  return y ? gcd(y,x%y) : x;
}

int main(){
  int n,i,co;
  cin >> n;
  vector<int> a(n);
  for(i=0;i<n;++i){
    cin >> a[i];
  }
  vector<int> l(n),r(n);

  for(i=0;i<n-1;++i){
    l[i+1]=gcd(l[i],a[i]);
  }
  for(i=n-1;i>=1;--i){
    r[i-1]=gcd(r[i],a[i]);
  }
  int ans=1;
  for(i=0;i<n;++i){
    ans=max(ans,gcd(l[i],r[i]));
  }
  cout << ans << endl;
  return 0;
}
