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 = Integer.parseInt(sc.next());
        int[] a = new int[n];
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(sc.next());
        }
        
        int[] b = new int[n];
        int[] c = new int[n];
        b[0] = a[0];
        c[n-1] = a[n-1];
        for(int i=0; i<n-1; i++){
            b[i+1] = gcd(b[i], a[i+1]);
            c[n-2-i] = gcd(c[n-1-i], a[n-2-i]);
        }
        
        int max = Math.max(c[1], b[n-2]);
        for(int i=0; i<n-2; i++){
            int tmp = gcd(b[i], c[i+2]);
            max = Math.max(tmp, max);
        }
        
        System.out.println(max);
        
    }
    
    public static int gcd(int a,int b){
        return b>0?gcd(b,a%b):a;
    }
}
