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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            //int[] A = new int[N];
            var A = System.Console.ReadLine()
                    .Split(' ')
                    .Select(s => int.Parse(s))
                    .ToArray();
            int count = 0;

            List<int> GcdList = new List<int>();

            for (int i = 0; i < N; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    int temp = GcdRecursive(A[i], A[j]);
                    if (temp != 1)
                    {
                        GcdList.Add(temp);
                    }
                }
            }


            Console.WriteLine(GcdList.Max());
        }

        private static int GcdRecursive(int a, int b)
        {
            return b == 0 ? a : GcdRecursive(b, a % b);
        }
    }
}