Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
 
using namespace std;
 
int calc_Greatest_common_divisor(int n, int m)
{
  while (n % m != 0)
  {
    int temp = m;
    m = n % m;
    n = temp;
  }
  return m;
}

void GCDonBlackboard()
{
  int n;
  cin >> n;
  vector<int> a(n);
 
  for (int i = 0; i < n; i++)
  {
    cin >> a[i];
  }
  sort(a.begin(), a.end());
  
 
  int max = 0;
  for (int i = 0; i < a.size(); i++)
  {
    for (int j = i+1; j < a.size(); j++)
      if (max < calc_Greatest_common_divisor(a[i], a[j])) max = calc_Greatest_common_divisor(a[i], a[j]);
  }
  cout << max << endl;
  return;
}
 
 
int main()
{
  GCDonBlackboard();
}