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.*;
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 < n ; i++){
                        a[i] = sc.nextInt();
                }
                sc.close();
                Arrays.sort(a);
                int yono = 0;
                for(int i = a[1] ; i > 0 && yono == 0 ; i--){
                        int che = 0;
                        for(int j = 0 ; j < n && che != 2 ; j++){
                                if(a[j] % i != 0) che++;
                        }
                        if(che != 2) yono = i;
                }
                System.out.println(yono);
        }
}