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;

public class Main {

    public static void main(String[] args) {
	// write your code here
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int a[] = new int[n];
        Arrays.setAll(a, i -> scanner.nextInt());
        int left[] = new int[n], right[] = new int[n];

        for (int i = 1; i < n; i ++) left[i] = gcd(left[i - 1], a[i - 1]);
        for (int i = n - 2; i >= 0; i --) right[i] = gcd(right[i + 1], a[i + 1]);

        int res = 1;
        for (int i = 0; i < n; i ++) res = Math.max(res, gcd(left[i], right[i]));

        System.out.println(res);

    }

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