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{
		
	public static void main(String args[]){
		  
	    Scanner sc = new Scanner(System.in);
	    
	    int n = sc.nextInt();
	    int a[] = new int[n];
	    int ri[] = new int[n];
	    int le[] = new int[n];
	    
	    for(int i = 0; i < n; i++) {
	    	a[i] = sc.nextInt();
	    }
	    
	    int ans = 0;
	    le[0] = 0;
	    for(int i = 1; i < n; i++) {
	    	le[i] = gcd(le[i-1], a[i-1]);
	    }
	    
	    ri[n-1] = 0;
	    for(int i = n-2; i >= 0; i--) {
	    	ri[i] = gcd(ri[i+1], a[i+1]);
	    }
	    
	    for(int i = 0; i < n; i++) {
	    	ans  = Math.max(ans, gcd(le[i], ri[i]));
	    }
	    
	    System.out.println(ans);
	}
	  
	public static int gcd(int n, int m) {
		if(m == 0) {
			return n;
		}else {
			return gcd(m, n%m);
		}
	}
}