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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int D = -1;

        int[] mas = new int[n];
        for (int i = 0; i < n; i++) {
            mas[i] = scanner.nextInt();
        }

        if (n == 1) {
            System.out.println("0");
            return;
        }

        boolean flag = true;
        ArrayList<Integer> shareAnswers = new ArrayList<>();

        for (int i = 0; flag && i <= Arrays.stream(mas).max().getAsInt(); i++) {
            for (int j = 0; j < mas.length; j++) {

                if (shareAnswers.size() == 0) {
                    shareAnswers.add(mas[j] + i);
                    shareAnswers.add(mas[j] - i);
                    shareAnswers.add(mas[j]);
                    continue;
                }

                boolean e = shareAnswers.retainAll(Arrays.asList(mas[j] + i, mas[j] - i, mas[j]));
                if (shareAnswers.size() != 0) {
                    if (j == mas.length - 1) {
                        D = i;
                        flag = false;
                    }
                    continue;
                }
                if (e)
                    break;
            }
        }

        System.out.println(D);


    }
}
