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 scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int[] a = new int[n];
        int[] forward = new int[n + 1];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
            forward[i + 1] = gcd(a[i], forward[i]);
        }

        int best = forward[n];
        int current = 0;
        for (int i = 1; i < n; i++) {
            best = Math.max(best, gcd(current, forward[n - i]));
            current = gcd(current, a[n - i]);
        }
        best = Math.max(best, current);
        System.out.println(best);
    }

    private static int gcd(int a, int b) {
        int min = Math.min(a, b);
        int max = Math.max(a, b);
        if (min == 0) return max;
        return gcd(min, max % min);
    }
}