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.io.*;

import java.util.*;

public class CodeForce {
 static int[] inputarr(String[] str){
     int[] arr=new int[str.length];
     for(int i=0;i<str.length;i++)
         arr[i]=Integer.parseInt(str[i]);
     
     return arr;
 }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        
        
        
        int n=Integer.parseInt(br.readLine());
       int[] arr=inputarr(br.readLine().split(" "));
       Set<Integer> set=new HashSet<>();
      
           for(int i=0;i<n;i++){
               set.add(arr[i]);
           }
            ArrayList<Integer> a=new ArrayList<>(set);
             Collections.sort(a);
           if(set.size()>3)
               System.out.println(-1);
           else if(set.size()==1)
               System.out.println(0);
           else if(set.size()==2){
              
               int y=a.get(1)-a.get(0);
               if(y%2==0)
                   System.out.println(y/2);
               else
                   System.out.println(y);
           }
           else{
              
               int x=a.get(0);
               int y=a.get(1);
               int z=a.get(2);
               if(y-x==z-y)
                   System.out.println(y-x);
                 else
                   System.out.println(-1);
               
           }
       
}}