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.*;

public class cf1154b {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        int[] a = new int[n];

        int min = Integer.MAX_VALUE;
        int max = Integer.MIN_VALUE;
        Set<Integer> set = new HashSet<Integer>();

        for (int i = 0; i < n; i++) {

            int x = in.nextInt();
            set.add(x);

            max = Math.max(x, max);
            min = Math.min(x, min);

        }
        
        if (set.size() == 2) {
            if ((max - min) % 2 != 0) {
                System.out.println(max - min);
            } else {
                System.out.println((max - min) / 2);
            }
        }

        if (set.size() > 3) {
            System.out.println(-1);
            return;
        }

        

        if (set.size() == 1) {
            System.out.println(0);
            return;
        }

        if (set.size() == 3) {

            int mid = -1;
            for (Integer integer : set) {

                if (integer == max || integer == min) {
                    continue;
                }
                mid = integer;

            }

            if (mid - min == max - mid) {
                System.out.println(mid - min);
            } else {
                System.out.println(-1);
            }

        }

    }

}
