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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;


public class main {

    
    public static void main(String[] args) {
       int l,r,k,x=0,b=0,c,d,t,e=0,y,z;
        Scanner in=new Scanner(System.in);
        t=in.nextInt();
        ArrayList<Integer>a=new ArrayList<>();
        for(int i=0;i<t;i++)
        {
            a.add(in.nextInt());
        }
         List<Integer> m;
        m = a.stream() 
                .distinct() 
                .collect(Collectors.toList()); 
       Collections.sort(m);
        if(m.size()==1)
        {
            System.out.println("0");
            System.exit(0);
        }
        if(m.size()>3)
        {
            System.out.println("-1");
            System.exit(0);
        }
        if(m.size()==2)
        {
            z=((m.get(1)-m.get(0)));
            if(z%2==0)
            {
                System.out.println(z/2);
            }
            else{
                System.out.println(z);
            }
            System.exit(0);
        }
        //System.out.println(m);
        l=m.get(1)-m.get(0);
        r=m.get(2)-m.get(1);
        
        if(l==r)
        {
            System.out.println(l);
        }
        else
        {
            System.out.println("-1");
        }
        
    }
    
}
