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: Runtime Error)

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

namespace ABC125
{
    class Program
    {
        static long GCD(long a, long b)
        {
            return (a < b)? GCD(b, a):
                   (a % b == 0)? b:
                                 GCD(b, a % b);
        }

        static long Search(long[] A, int N, int idx)
        {
            int residx = idx;
            long resmin = A[idx];
            for (int i = 0; i < N; i++)
            {
                if (resmin > GCD(A[i], A[idx]))
                {
                    resmin = GCD(A[i], A[idx]);
                    residx = i;
                }
            }
            long res = A[idx];
            for (int i = 0; i < N; i++)
            {
                if (i == residx) continue;
                res = GCD(res, A[i]);
            }
            return res;
        }

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            long[] A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).OrderByDescending(x => x).ToArray();
            
            long res = Search(A, N, 0);
            long res2 = Search(A, N, 2);
            long res3 = A[0];
            for (int i = 0; i < N; i++)
                res3 = GCD(res3, A[i]);
            Console.WriteLine(Math.Max(Math.Max(res, res2), res3));
        }
    }
}