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.Arrays;
import java.util.Scanner;

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();
        }
        Arrays.sort(a);
        int ans = 1;
        for (int i = a[1]; i > 1; i--) {
            int cnt = 0;
            boolean ok = false;
            for (int j = 0; j < n; j++) {
                if (a[j] % i != 0) {
                    cnt++;
                }
                if (cnt > 1) {
                    break;
                }
                if (j == n - 1) {
                    ans = i;
                    ok = true;
                }
            }
            if (ok) {
                break;
            }
        }
        System.out.println(ans);
        sc.close();
    }
}