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.Arrays;
import java.util.Scanner;

public class Main {
	static int n;
	static long r,a,b,ans;
	static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		n=sc.nextInt();
		long A[]=new long[n];
		for(int i=0;i<n;i++)A[i]=sc.nextLong();
		Arrays.sort(A);
		ans=0;
		b=A[0];
		for(int i=1;i<n;i++) {
			long temp=gcd(A[i],b);
			if(ans<temp)ans=temp;
		}
		System.out.println(ans);
		}
	public static long gcd(long a,long b) {
		while ((r = a % b) != 0) {
			a = b;
			b = r;
			}
		return b;
	}
}