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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program {
    static void Main(string[] args) {
        //入力
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        int[] A = new int[N + 1];

        //変数の割り当て
        for (int i = 0; i < N; i++) {
            A[i] = int.Parse(s.Split(' ')[i]);
        }
        A[N] = 0;

        int[] L = new int[N + 1];
        L[0] = 0;
        int[] R = new int[N + 1];
        R[N] = 0;
        int[] M = new int[N + 1];

        //計算
        //[0, i)の最大公約数を計算する
        for (int i = 0; i < N; i++) {
            L[i + 1] = GCD(L[i], A[i]);
        }

        //(i, N]の最大公約数を計算する
        for (int i = N - 1; i >= 0; i--) {
            R[i] = GCD(R[i + 1], A[i]);
        }

        //M[i]を求める
        for (int i = 0; i < N; i++) {
            M[i] = GCD(L[i], R[i + 1]);
        }

        //M[i]の中で最大のものをこたえる

        Console.WriteLine(M.Max());
    }







    //ユークリッドの互除法
    public static int GCD(int num1, int num2) {

        if (num1 < num2) {
            return GCD(num2, num1);
        }

        if (num2 == 0) {
            return num1;
        }
        if (num1 == 0) {
            return num2;
        }

        //計算時の余りを格納する変数
        int num3 = 0;

        while (true) {
            num3 = num1 % num2;
            num1 = num2;
            num2 = num3;

            if (num3 == 0) break;

        }


        int result = num1;

        return result;
    }
}