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 <iostream>
#include <vector>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;

int gcd(int x, int y) {
  if (y == 0) return x;
  return gcd(y, x%y);
}

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