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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp5
{

    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string S = Console.ReadLine();
            string[] line = S.Split(' ');
            int[] A = new int[N];
            int ans = 1;
            int count = 0;
            for(int i = 0; i < N; i++)
            {
                A[i] = int.Parse(line[i]);
            }
            for (int i = 2; i < A.Max(); i++)
            {
                for (int j = 0; j < N; j++)
                {
                    if(A[j] % i != 0)
                    {
                        count++;
                    }

                    if(count == 2)
                    {
                        break;
                    }
                    
                }
                if(count < 2)
                {
                    ans = i;
                }
                count = 0;

            }
            Console.WriteLine(ans);


        }
    }
}