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 a[] = new int[n];
        int left[] = new int[n+1]; //左からの累積GCD配列
        int right[] = new int[n+1]; //右からの累積GCD配列
        
        for(int i=0; i<n; i++){
            a[i] = sc.nextInt();
        }
        for(int i=0; i<n; i++){
            left[i+1] = gcd(left[i], a[i]);
        }
        for(int i=n-1; i >= 0; i--){
            right[i] = gcd(right[i+1], a[i]);
        }

        int gcd_max = 0;
        for(int i=0; i<n; i++){
            gcd_max = Math.max(gcd(left[i],right[i+1]),gcd_max);
        }
        System.out.println(gcd_max);
    }
    static int gcd(int a, int b){
        if(b==0) return a;
        else return gcd(b, a%b);
    }
}