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 {
    int gcd(int a, int b) {
        if (a > b) return gcd(b, a);
        if (a == 0) return b;
        return gcd(b % a, a);
    }

    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] as = new int[n];
        for (int i = 0; i < n; i++) {
            as[i] = sc.nextInt();
        }

        int[] ls = new int[n];
        int[] rs = new int[n];
        for (int i = 0; i < n; i++) {
            int j = n - i - 1;
            if (i == 0) {
                ls[i] = as[i];
                rs[j] = as[j];
            } else {
                ls[i] = gcd(ls[i - 1], as[i]);
                rs[j] = gcd(rs[j + 1], as[j]);
            }
        }
        int ans = 0;
        for (int i = 0; i < n; i++) {
            if (i == 0) {
                ans = Math.max(ans, rs[1]);
            } else if (i == n - 1) {
                ans = Math.max(ans, ls[n - 2]);
            } else {
                ans = Math.max(ans, gcd(ls[i - 1], rs[i + 1]));
            }
        }
        System.out.println(ans);
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
