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 GCD_on_Blackboard
{
    class Program
    {
        //euclidean algorithm
        static int GCD (int[] a)
        {
            for (int i = 1; i < a.Length; i++)
            {
                while (a[0] != a[i]) 
                {
                    if (a[0] > a[i])
                    {
                        a[0] = a[0] - a[i];
                    }
                    else
                    {
                        a[i] = a[i] - a[0];
                    }
                }        
            }
            return a[0];
        }
        static void Main(string[] args)
        {
            int n = Convert.ToInt32(Console.ReadLine());
            string[] temp = Console.ReadLine().Split(' ');
            int[] A = new int[n];
            for (int i = 0; i< n;i++)
            {
                A[i] = Convert.ToInt32(temp[i]);
            }

            int[] tofunc = new int[n];
            int gcd = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n-1; j++)
                {
                    tofunc[j] = A[(i + j) % n];
                }
                if (gcd < GCD(tofunc))
                {
                    gcd = GCD(tofunc);
                }
            }

            Console.WriteLine(gcd);
            Console.ReadKey();
        }
    }
}