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{
	
	static int gcd(int a, int b){
		if(a<b){
			int temp= a;
			a=b;
			b=temp;
		}
		if(b==0) return a;
		return gcd(a%b,b);
	}
	
	
	public static void main(String []args){
	    Scanner sc= new Scanner(System.in);
	    
		int n=sc.nextInt();
		int[] A = new int [n];
		int[] L = new int [n];
		int[] R = new int [n];
		
		for(int i=0;i<n; i++){
		    A[i]=sc.nextInt();
		}
		
		L[0]=0;
		R[0]=0;
		
		for (int i=1; i<n; i++){
		    L[i]=gcd(L[i-1],A[i-1]);
		    R[i]=gcd(R[i-1],A[n-i]);
		}
		
		int gcd=0;
		
		for (int i=0; i<n; i++){
		    int temp=gcd(L[i], R[n-i-1]);
		    
		    if(gcd<temp){
		        gcd=temp;
		    }
		    
		}
		System.out.println(gcd);
		
    }
}
