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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int ans = 0;

            int N = int.Parse(Console.ReadLine());

            string[] s = Console.ReadLine().Split(' ');

            int[] A = new int[N];

            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(s[i]);
            }

            Array.Sort(A);

            ans = A[1];

            for(ans = A[1];ans > 0;ans--)
            {
                int check = 0;
         

                for(int i=0;i<N;i++)
                {
                    if(A[i] % ans != 0)
                    {
                        check++;
                    }

                    if (check > 1)
                        break;
                }

                if(check < 2)
                    break;

            }
            Console.WriteLine(ans.ToString());
        }
    }
}