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.

Examples

Input

3
7 6 8


Output

2


Input

3
12 15 18


Output

6


Input

2
1000000000 1000000000


Output

1000000000
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int[] a = new int[n];

        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(sc.next());
        }

        int[] l = new int[n + 1];
        int[] r = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            l[i] = gcd(l[i - 1], a[i - 1]);
            r[n - i] = gcd(r[n + 1 - i], a[n - i]);
        }

        int result = 0;
        for (int i = 0; i < n; i++) {
            result = Math.max(result, gcd(l[i], r[i + 1]));
        }

        System.out.println(result);
    }

    private static int gcd(int a, int b) {
        return b > 0 ? gcd(b, a % b) : a;
    }
}
