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.*;

class Main{
    public static void main(String[] args){
        
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] A = new int[N];
        int[] L = new int[N + 1];
        int[] R = new int[N + 1];
        L[0] = 0;
        R[N] = 0;

        for(int i=0; i<N; i++){
            A[i] = sc.nextInt();
        }
        int max = 0;
        for(int i=0; i<N; i++){
            for(int j=0; j<i; j++){
                if(j==0){
                    L[j + 1] = A[j];
                    continue;
                }
                L[j + 1] = getCommonDivisor(L[j], A[j]);
            }
            for(int j=N-1; j>i; j--){
                if(j==N-1){
                    R[j] = A[j];
                    continue;
                }
                R[j] = getCommonDivisor(R[j + 1], A[j]);
            }
            if(i==0){
                max = Math.max(max, R[i + 1]);
                continue;
            }
            if(i==N-1){
                max = Math.max(max, L[i]);
                continue;
            }
            max = Math.max(max, getCommonDivisor(L[i], R[i + 1]));
        }
        System.out.println(max);
    }

    

    private static int getCommonDivisor(int x, int y){
        int bigger = Math.max(x, y);
        int smaller = Math.min(x, y);
        int surplus = bigger % smaller;
        
        if(surplus==0){
            return smaller;
        }
        surplus = getCommonDivisor(smaller, surplus);

        return surplus;
    }
}