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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Type;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.logging.SocketHandler;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        String[] line = reader.readLine().split(" ");
        int[] a = new int[line.length];

        int max = 0;
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < line.length; i++) {
            a[i] = Integer.parseInt(line[i]);
            if (a[i] > max) max = a[i];
            if (a[i] < min) min = a[i];
        }
        int k = max - min;

        if (k % 2 == 1){
            for (int i = 0; i < a.length; i++) {
                if (!(a[i] == min || a[i] == max)) {
                    System.out.println("-1");
                    return;
                }
            }
            System.out.println(k);
            return;
        } else {
            for (int i = 0; i < a.length; i++) {
                if (!(a[i] == min || a[i] == max || a[i] + k / 2 == max)) {
                    System.out.println("-1");
                    return;
                }
            }
            System.out.println(k / 2);
            return;
        }

    }
}