You are given a sequence a_1, a_2, ..., a_n consisting of n integers.

You can choose any non-negative integer D (i.e. D ≥ 0), and for each a_i you can:

  * add D (only once), i. e. perform a_i := a_i + D, or 
  * subtract D (only once), i. e. perform a_i := a_i - D, or 
  * leave the value of a_i unchanged. 



It is possible that after an operation the value a_i becomes negative.

Your goal is to choose such minimum non-negative integer D and perform changes in such a way, that all a_i are equal (i.e. a_1=a_2=...=a_n).

Print the required D or, if it is impossible to choose such value D, print -1.

For example, for array [2, 8] the value D=3 is minimum possible because you can obtain the array [5, 5] if you will add D to 2 and subtract D from 8. And for array [1, 4, 7, 7] the value D=3 is also minimum possible. You can add it to 1 and subtract it from 7 and obtain the array [4, 4, 4, 4].

Input

The first line of the input contains one integer n (1 ≤ n ≤ 100) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100) — the sequence a.

Output

Print one integer — the minimum non-negative integer value D such that if you add this value to some a_i, subtract this value from some a_i and leave some a_i without changes, all obtained values become equal.

If it is impossible to choose such value D, print -1.

Examples

Input


6
1 4 4 7 4 1


Output


3


Input


5
2 2 5 2 5


Output


3


Input


4
1 3 3 7


Output


-1


Input


2
2 8


Output


3

import java.util.*;

public class GFG {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n]; 
		int d = -1;
		
		
		for (int i = 0; i < n; i++)
		{
		    a[i] = sc.nextInt();
		}
		
		
		boolean cont = true;
		
		Arrays.sort(a);
		
		if ((a[n-1] - a[0]) % 2 == 0)
		{
		    d = (a[n-1] - a[0])/2;

		    for (int i = 1; (i < n-1) && cont; i++)
		    {
		        
		        if (((a[n-1] - d) == a[i]) && ((a[0] + d) == a[i]))
		        {
		            
		        }
		        else if (a[n-1] == a[i])
		        {
		            
		        }
		        else if (a[0] == a[i])
		        {
		            
		        }
		        else
		        {
		            d = -1;
		            cont = false;
		        }
		        
		    }
		}
		else if ((a[n-1] - a[0]) % 2 == 1)
		{
		    
		    d = (a[n-1] - a[0]);
		    
		    for (int i = 1; (i < n-1) && cont; i++)
		    {
	            if (a[n-1] == a[i])
	            {
	               
	            }
	            else if (a[0] == a[i])
	            {
    	          
    	        }
    	        else
    	        {
    	            d = -1;
    	            cont = false;
    	        }
		    }
		}
		System.out.println(d);
	}
}