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 main() {
  int N;
  cin >> N;
  multiset<long> A;
  long temp;
  for (int i = 0; i < N; i++) {
    cin >> temp;
    A.insert(temp);
  }
  int count;
  long j;
  for (j = *(++A.begin()); j > 0; j--) {
    count = 0;
    for (auto a : A) {
      if (a % j != 0) count++;
      if (count > 1) break;
    }
    if (count < 2) break;
  }
  cout << j;
  return 0;
}