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.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        int n;
        int ans = 0;
        int[] a;
        int[] front_gcd;
        int[] back_gcd;

        n = Integer.parseInt(sc.next());
        a = new int[n + 5];
        front_gcd = new int[n + 5];
        back_gcd = new int[n + 5];

        for (int i = 1; i <= n; i++) {
            a[i] = Integer.parseInt(sc.next());
        }

        for (int i = 1; i <= n; i++) {
            front_gcd[i] = gcd(front_gcd[i - 1], a[i]);

        }

        for (int i = n; i >= 1; i--) {
            back_gcd[i] = gcd(back_gcd[i + 1], a[i]);

        }

        for (int i = 1; i <= n; i++) {
            ans = Math.max(ans, gcd(front_gcd[i - 1], back_gcd[i + 1]));
        }

        System.out.println(ans);
    }

    public static int gcd(int x, int y) {
        int n = Math.min(x, y);
        int m = Math.max(x, y);

        while (n > 0) {
            int r = m % n;
            m = n;
            n = r;
        }

        return m;
    }

}
