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