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 sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] arr = new int[N];
        for(int i = 0; i < N;i ++) arr[i] = sc.nextInt();

        long[] left = new long[N+1];
        long[] right = new long[N+1];
        for(int i = 0; i < N; i++) {
            left[i+1] = gcd(left[i], arr[i]);
        }
        for(int i = N-1; i >= 0; i--) {
            right[i] = gcd(right[i+1], arr[i]);
        }
        long res = 0;
        for(int i = 0; i < N; i++) {
            int l = (int)left[i];
            int r = (int)right[i+1];
            res = Math.max(res, gcd(l,r));
        }
        System.out.println(res);
    }
    public static long gcd(long a, long b) {
        if(b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }
}
