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
//I AM THE CREED
/* //I AM THE CREED
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
 
public class HelloWorld{
    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        while(input.hasNext()){
            int n=input.nextInt();
            HashSet<Integer> s=new HashSet<>();
            int max=Integer.MIN_VALUE;
            int min=Integer.MAX_VALUE;
            for(int i=0;i<n;i++){
                int ele=input.nextInt();
                max=Math.max(max, ele);
                min=Math.min(min, ele);
                s.add(ele);
            }
            if(s.size()>3){
                System.out.println(-1);
                continue;
            }    
            if(s.size()==1){
                System.out.println(0);
                continue;
            }
            if(s.size()==2){
                if((min-max)%2==0){
                    System.out.println((max-min)/2);
                    continue;
                }
                System.out.println(max-min);
                continue;
            }
            if(s.size()==3){
                int middle=-1;
                for(int ele:s){
                    if(ele!=min && ele!=max){
                        middle=ele;
                        break;
                    }
                }
                if((max-min)%2==0 && (max+min)/2==middle){
                    System.out.println((max-min)/2);
                    continue;
                }
                System.out.println(-1);
            }
            
        }
    }
}