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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.nextLine());
		String[] list = sc.nextLine().split(" ",0);
		int gcd;
		int a1;
		int tmp;
		int x,y;
		List<Integer> gcdList = new ArrayList<>();
		for (int i=0;i<N;i++) {
			if (i == 0) {
				gcd = Integer.parseInt(list[1]);
			} else {
				gcd = Integer.parseInt(list[0]);
			}
			for (int j=0; j<N; j++) {
				if (j == i) {
					//
				} else {
					a1 = Integer.parseInt(list[j]);
					if (gcd < a1) {
						x = a1;
						y = gcd;
					} else {
						x = gcd;
						y = a1;
					}
					while ((tmp = x % y) != 0) {
						x = y;
						y =tmp;
					}
					gcd = y;
				}
			}
			gcdList.add(gcd);

		}
		int max = Collections.max(gcdList);
		System.out.println(max);
		sc.close();
	}

}