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 po[]=new int[n];
        int gcd1[]=new int[n];
        int gcd2[]=new int[n];
        for(int i=0;i<n;i++){
            po[i]=sc.nextInt();
        }
        for(int i=0;i<n;i++){
            if(i==0)gcd1[0]=po[0];
            else{
                gcd1[i]=gcd(gcd1[i-1],po[i]);
            }
        }
        for(int i=n-1;i>=0;i--){
            if(i==n-1)gcd2[n-1]=po[n-1];
            else{
                gcd2[i]=gcd(gcd2[i+1],po[i]);
            }
        }
        int max=0;
        for(int i=0;i<n;i++){
            if(i==0)max=Math.max(max,gcd2[1]);
            else if(i==n-1)max=Math.max(max,gcd1[n-2]);
            else{
                max=Math.max(max,gcd(gcd1[i-1],gcd2[i+1]));
            }
        }
        
        System.out.println(max);
    }
    public static int gcd(int m, int n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }
}