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;

public class ABC0125_A3v2 {
    private static void Main(string[] args) {
        var inputs = new List<string>(){
            Console.ReadLine().Trim(),
            Console.ReadLine().Trim(),
        };
        Prepare(inputs);
    }

    private static void Prepare(List<string> inputs) {
        var numbersStr = inputs[1].Split();
        var numbers = ConvertStrsToIntList(numbersStr).OrderBy(n => n).ToList();
        Compute(numbers);
    }

    private static void Compute(List<int> numbers) {
        var maxOfGCDs = 0;

        for (var index = 0; index < numbers.Count; index++) {
            var tempNumbers = new List<int>(numbers);
            tempNumbers.RemoveAt(index);

            var currentGCD = GetGcdFromOrderedInts(tempNumbers.Distinct());
            maxOfGCDs = Math.Max(maxOfGCDs, currentGCD);
        }

        OutputAnswer(maxOfGCDs.ToString());
    }

    private static void OutputAnswer(string text) => Console.WriteLine(text);
    private static List<int> ConvertStrsToIntList(IEnumerable<string> texts) => texts.Select(x => int.Parse(x)).ToList();
    private static int CalcGCD(int a, int b) => b == 0 ? a : CalcGCD(b, a % b);
    private static int GetGcdFrom2Ints(int a, int b) => a > b ? CalcGCD(a, b) : CalcGCD(b, a);

    private static int GetGcdFromOrderedInts(IEnumerable<int> orderedNumbers) {
        for (var indexL = 0; indexL < orderedNumbers.Count() - 1; indexL++) {
            for (var indexH = indexL; indexH < orderedNumbers.Count(); indexH++) {
                var currentCD = GetGcdFrom2Ints(orderedNumbers.ElementAt(indexL), orderedNumbers.ElementAt(indexH));

                if (IsCD(orderedNumbers, currentCD))
                    return currentCD;
            }
        }
        return orderedNumbers.First();
    }

    private static bool IsCD(IEnumerable<int> numbers, int divisor) {
        if (divisor <= 0) {
            return false;
        }

        foreach (var number in numbers) {
            if (number % divisor != 0)
                return false;
        }

        return true;
    }
}