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.*;
import java.math.*;


public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] list = new int[N];
        for(int i=0;i<N;i++){
            list[i] = Integer.parseInt(sc.next());
        }
        int[] listA = new int[N];
        int[] listB = new int[N];
        listA[0] = list[0];
        listB[N-1] = list[N-1];
        for(int i=1;i<N;i++){
            listA[i] = gcd(listA[i-1],list[i]);
            listB[N-1-i] = gcd(listB[N-i], list[N-i-1]); 
        }
        int ans = 0;
        for(int i=0;i<N;i++){
            if(i==0){
                ans= Math.max(ans,listB[i+1]);
            }else if(i==N-1){
                ans= Math.max(ans,listA[i-1]);
            }else{
                ans= Math.max(ans,gcd(listA[i-1],listB[i+1]));
            }
        }
        System.out.println(ans);
    }
    static int gcd (int a, int b) {return b>0?gcd(b,a%b):a;}
}

