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: Accepted)

using System;
using System.Linq;

    class Program
    {
        static int Gcd(int a,int b)
        {
            if (a < b)
            {
                var t = a;
                a = b;
                b = t;
            }
            if (b == 0) return a;
            return Gcd(b, a % b);
        }

        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var inArr = new int[N + 2];
            var pref = new int[N + 2];
            var suf = new int[N + 2];

            var inputs = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

            for (var i = 1;i<=N;i++)
            {
                inArr[i]= inputs[i-1];
                pref[i]= Gcd(pref[i - 1], inArr[i]);
            }

            for (var i = N; i >= 1; i--)
            {
                suf[i] = Gcd(suf[i + 1], inArr[i]);
            }
            var max = 0;
            for (var i = 1; i <=N; i++)
            {
                max = Math.Max(max, Gcd(pref[i - 1], suf[i + 1]));
            }
            Console.WriteLine(max);
        }
    }