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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		int[] A = new int[N];
		for(int i = 0; i < N ; i++) {
			A[i] = sc.nextInt();
		}

		A[0] = A[1];

		sc.close();

		int answer = gcd(A[0],A[1]);

		for(int i = 1 ; i < N - 1 ;i ++) {
			answer = gcd(answer, A[i+1]);
		}

		System.out.println(answer);
	}

	public static int gcd(int a, int b) {
		int tmp;
		if(b > a) {
			tmp = a;
			a = b;
			b = tmp;
		}

	    int r = -1;
	    while (r != 0) {
	        r = a % b;
	        a = b;
	        b = r;
	    }

	    return a;
	}

}