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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] A = new int[N];
        for (int i = 0; i < A.length; ++i) {
            A[i] = sc.nextInt();
        }

        System.out.println(solve(A));

        sc.close();
    }

    static int solve(int[] A) {
        Set<Integer> divisors = new HashSet<>();
        for (int i = 0; i < 2; ++i) {
            for (int j = 1; j * j <= A[i]; ++j) {
                if (A[i] % j == 0) {
                    divisors.add(j);
                    divisors.add(A[i] / j);
                }
            }
        }

        return divisors.stream()
                .filter(divisor -> Arrays.stream(A).filter(x -> x % divisor == 0).count() >= A.length - 1)
                .mapToInt(x -> x).max().getAsInt();
    }
}