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>
#include <math.h>
#include <algorithm>
using namespace std;
int main() {
  int n; cin >> n;
  vector<int> a(n, 0);
  for (int i=0; i<n; i++) cin >> a.at(i);
  sort(a.begin(), a.end());
  int r=1;
  for (int i=a.at(1); i>0; i--) {
    int s = 0;
    for (int j=0; j<n; j++) {
      if (a.at(j) % i != 0) {
        s++;
        if (s==2) break;
      }
    }
    if (s<=1) {r=i; break;}
  }
  cout << r << endl;
}