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.stream.*;
import java.util.*;

public class Main {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int n = scanner.nextInt();
        int[] a = IntStream.range(0, n).map(i -> scanner.nextInt()).toArray();
        int[] gcd = new int[n];
        int[] temp = new int[n];

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

        Arrays.stream(gcd).max().ifPresent(System.out::println);
    }

    public static int gcd(int a, int b) {
        return 0 < b ? gcd(b, a % b) : a;
    }
}