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;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(Console.ReadLine());
        var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var last = input.Last();
        
        var a = input.Count(d => d == last);
        if (a == 1) {
           Console.WriteLine(input[0]); 
           return;
        }
        var b = input.Count(d => d == input[0]);
        if (b == 1) {
            Console.WriteLine(last);
            return;
        }
        
        var list = new List<int>();
        if (N == 2) {
            var target = input[0] >= input[1] ? input[0] : input[1];
            Console.WriteLine(target);
        } else {
            for (var i = 1; i <= last / 2; i++) {
                if (last % i == 0) {
                    list.Add(i);
                }
            }
            
            list.Add(last);
            list.Reverse();
            var target = 1;
            for (var i = 0; i < list.Count; i++) {
                var cnt = hoge(input, list[i]);
                if (cnt <= 1) {
                    target = list[i];
                    break;
                }
            }            
            Console.WriteLine(target);
        }
    }
    
    public static int hoge(int[] input, int target) {
        var cnt = 0;
        for (var i = 0; i < input.Length - 1; i++) {
            if (input[i] % target != 0) {
                cnt++;
            }
            if (cnt > 1) break;
        }
        return cnt;
    }
}