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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        int[] values = new int[n];
        int[] lefts = new int[n];
        int[] rights = new int[n];

        for (int i = 0; i < n; i++) {
            values[i] = sc.nextInt();
        }

        int result = 0;

        for (int i = 0; i < n; i++) {
            int current = 0;
            for (int j = 0; j < n; j++) {
                if (i==j) {
                    continue;
                }
                current = gcd(current, values[j]);
            }

            result = current > result ? current : result;
        }

        System.out.println(result);
    }

    private static int gcd(int m, int n) {
        if (n == 0) {
            return m;
        }
        int tmp = m % n;
        return gcd(n, tmp);
    }
}