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 in = new Scanner(System.in);
        int n = in.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; ++i){
            a[i] = in.nextInt();
        }
        Arrays.sort(a);

        int max = a[1];
//        System.out.println("max: " + max);
    
        for (int i = max; i >= 1 ; i--){
//            System.out.println("i: " + i);
            int count = 0;
            for (int j = 0; j < n; ++j){
                if (a[j]%i != 0){
                    count++;
                }
            }
//            System.out.println("count: " + count);
            if (count == 1 || count == 0){
                System.out.println(i);
                break;
            }
        }
    }
}
