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>
#define r(i,n) for(int i = 0; i<n; i++)
using namespace std;

int gcd(int a, int b){
  if(b==0)return a;
  else return gcd(b,a%b);
}

int main() {
  int n,ans=1;
  cin >> n;
  vector<int> v(n),l(n,0),q(n,0);
  r(i,n)cin>>v[i];
  r(i,n-1)l[i+1]=gcd(l[i],v[i]);
  r(i,n-1)q[n-i-2]=gcd(q[n-i-1],v[n-i-1]);
  r(i,n)ans=max(ans,gcd(l[i],q[i]));
  cout << ans << endl;
}
