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
//package codeforces.r552_1154;

import java.util.Arrays;
import java.util.Scanner;

public class B {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int[] numbers = new int[N];
        int[] uniqueNumbers = new int[N];
        for (int i = 0; i < N; i++) {
            numbers[i] = scanner.nextInt();
        }
        Arrays.sort(numbers);
        int index = 0;
        int currentValue = numbers[0];
        uniqueNumbers[index++] = currentValue;
        for (int i = 1; i < N; i++) {
            if (currentValue != numbers[i]) {
                uniqueNumbers[index++] = numbers[i];
                currentValue = numbers[i];
            }
        }
        if (index>3) {
            System.out.println(-1);
        } else {
            if (index==1) {
                System.out.println(0);
            } else if (index==2) {
                int diff = uniqueNumbers[1] - uniqueNumbers[0];
                if (diff%2==0) System.out.println(diff/2);
                else System.out.println(diff);
            } else {
                if (uniqueNumbers[1]-uniqueNumbers[0] == uniqueNumbers[2] - uniqueNumbers[1]) {
                    System.out.println(uniqueNumbers[1]-uniqueNumbers[0]);
                } else {
                    System.out.println(-1);
                }
            }
        }

    }
}
