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(final String[] args) {

        try (final 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();
            }
            int[] left = new int[N + 1];
            int[] right = new int[N + 1];
            for (int i = 0; i < N; i++) {
                left[i + 1] = gcd(left[i], A[i]);
            }
            for (int i = N - 1; i >= 0; i--) {
                right[i] = gcd(right[i + 1], A[i]);
            }
            int max = 0;
            for (int i = 0; i < N; i++) {
                max = Math.max(max, gcd(left[i], right[i + 1]));
            }
            System.out.println(max);
        }
    }

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