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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var aLine = Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();

            var one = aLine[0];
            var max = 0;
            var minIndex = new int[2];

            for (var i = 0; i < n; i++)
            {
                // i番目を含まない状態で回した中で最も大きい値を探す
                if (n > 2)
                    max = Math.Max(ReGcd(aLine.Where((name, index) => index != i).ToArray()), max);
                else
                    max = ReGcd(aLine);
            }

            Console.WriteLine(max);
        }

        static int Gcd(int m, int n)
        {
            if (n > m) return Gcd(n, m);
            if (n == 0) return m;
            return Gcd(n, (m % n));
        }

        static int ReGcd(int[] line)
        {
            var one = line[0];
            var min = int.MaxValue;
            var gcdValue = 0;
            for (var i = 1; i < line.Length; i++)
            {
                gcdValue = Gcd(one, line[i]);

                if (gcdValue < min)
                {
                    min = gcdValue;
                }
                one = gcdValue;
            }

            return min;
        }
    }
}