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
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.util.Scanner;

/**
 *
 * @author Centrino
 */
public class NewMain {

    /**
     * @param args the command line arguments
     */
 static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }
      
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
       int n =sc.nextInt();
       int arr[]=new int[n];
         for (int i = 0; i < n; i++) {
            arr[i]=sc.nextInt();
        }
       
         for (int i = 0; i <=100; i++) {
             boolean f=true;
             for (int j = 0; j < n; j++) {
                 
                 for (int k = j+1; k < n; k++) {
                    if((Math.abs(arr[k]-arr[j])!=i&&Math.abs(arr[k]-arr[j])!=2*i)&&arr[j]!=arr[k])
                    {
                    f=false;
                    break;
                    }
                 }
                 if(!f)
                 {break;}
             }
             if(f)
             {
                 System.out.println(i);
                 return ;
             
             }
        }
         System.out.println("-1");
    }
    
}
