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.Scanner;

public class Main {

    static int gcd(int a, int b){
        if(b == 0) return a;
        return gcd(b, a % b);
    }

    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] g = new int[n];
        int[] g2 = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
            if(i != 0) g[i] = gcd(g[i - 1], a[i]);
            else g[i] = a[i];
        }
        g2[n - 1] = a[n - 1];
        for(int i = n - 2; i >= 0; i--){
            g2[i] = gcd(g2[i + 1], a[i]);
        }
//        for(int i = 0; i < n; i++){
//            System.out.print(g2[i] + " ");
//        }
        int ans = Math.max(g2[1], g[n - 2]);
        for(int i = 1; i < n - 1; i++){
            int to = gcd(g[i - 1], g2[i + 1]);
            ans = Math.max(ans, to);
        }
        System.out.print(ans);
    }
}
