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;
using System.IO;
using static System.Console;
using static System.Math;

namespace AtCodeeeer
{
    class AtCOOOOOOOOOOOder
    {
        static void Main(string[] args)
        {
            int N = int.Parse(ReadLine());

            int[] An = ReadLine().Split(' ').Select(int.Parse).ToArray();

            var ls = new List<int>();
            ls.AddRange(An);
            int ans = 0;
            for (int i = 1; i < ls.Max(); i++)
            {
                if (Isprime(i))
                {
                    for (int j = 0; j < N; j++)
                    {
                        if (ls[j] % i != 0)
                        {
                            break;
                        }
                        else if (j == N-1)
                        {
                            ans = i;
                        }

                    }
                }
            }
            WriteLine(ans);

        }

        static public bool Isprime(int x)
        {
            if (x == 2)
            {
                return true;
            }
            if (x<2 || x % 2 == 0)
            {
                return false;
            }
            int i = 3;
            while (i <= Sqrt(x))
            {
                if (x % i == 0)
                {
                    return false;
                }
                i += 2;
            }
            return true;
        }
    }
}