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.*;
import java.util.stream.Collectors;

import static java.lang.Math.*;

public class Main {

    public static void main(String[] args) {
        new Solution().solve();
    }
}

class Solution {
    void solve() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Integer> temp = new ArrayList<>();
        for (int i = 0; i < n; i++)
            temp.add(sc.nextInt());
        List<Integer> list = temp.stream().distinct().collect(Collectors.toList());
        int D = -1;
        for (int i = 0; i <= 100; i++) {
            int d = -1;
            boolean fail = false;
            for (int e : list) {
                if (i == e) { if (d < 1) d = 0; }
                else if (d == -1 || d == 0) d = abs(i - e);
                else if (e + d != i && e - d != i) {
                    fail = true;
                    break;
                }
            }
            if (!fail) {
                assert d != -1;
                if (D == -1) D = d;
                else D = min(d, D);
            }
        }
        System.out.println(D);
    }
}