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.io.*;

class Main
{
  	static int gcd(int a, int b)
    {
      	int c = 0;
      while(b>0)
      {
        c = a;
        a = b;
        b = c%b;
      }
      return a;
    }
  	public static void main(String[] args)
    {
		Scanner s = new Scanner(System.in);
      	int n = s.nextInt();
      	int[] a = new int[n];
      	int[] b = new int[n];
      	int[] c = new int[n];
      	for(int i = 0 ; i<n ; i++)a[i] = s.nextInt();
      	int sum = 0;
      	b[0] = a[0];
      	for(int i = 1 ;  i<n ;i++)
        {
        	b[i] = gcd(b[i-1], a[i]); 	
        }
      	c[n-1] = a[n-1];
      	for(int i = n-2 ;  i>=0 ;i--)
        {
        	c[i] = gcd(c[i+1], a[i]); 	
        }
      	
      	int ans = 0;
		ans = Math.max(ans, c[1]);
      	ans = Math.max(ans, b[n-2]);
      	for(int i = 1 ;  i<n-1 ;i++)
        {
          	
        	ans = Math.max(ans, gcd(b[i-1], c[i+1]));
        }
      
      	System.out.println(ans);
    }
}