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
//  30/07/20  3:36 PM  Jul  2020 

import java.io.*;
import java.sql.SQLIntegrityConstraintViolationException;
import java.util.*;

public class _1154B {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n];
        HashSet<Integer> hset = new HashSet<>();
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
            hset.add(arr[i]);
        }
        ArrayList<Integer> l = new ArrayList<>(hset);
        boolean check = true;
        Collections.sort(l);
        if(l.size()==1)
            System.out.println("0");
        else if (l.size() == 2){
            int sum=l.get(1)+l.get(0);
            if(sum%2==0)
                System.out.println(l.get(1)-(l.get(1)+l.get(0))/2);
            else
                System.out.println(l.get(1)-l.get(0));
        }
        else {
            if (Math.abs(l.get(0) - l.get(1)) != Math.abs(l.get(2) - l.get(1)))
                check = false;

            if (hset.size() > 3 || !check)
                System.out.println("-1");
            else {
                System.out.println(Math.abs(l.get(0) - l.get(1)));
            }
        }
    }
}