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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author vinhvo
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BMakeThemEqual solver = new BMakeThemEqual();
        solver.solve(1, in, out);
        out.close();
    }

    static class BMakeThemEqual {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();

            int[] arr = new int[N];
            int max = Integer.MIN_VALUE;
            int min = Integer.MAX_VALUE;


            for (int i = 0; i < N; i++) {
                arr[i] = in.nextInt();
                max = Math.max(max, arr[i]);
                min = Math.min(min, arr[i]);
            }
            if (N == 1) {
                out.println(0);
                return;
            }

            boolean hasMid = false;
            for (int a : arr) {
                if (a != min && a != max) {
                    hasMid = true;
                    break;
                }
            }


            int D = hasMid ? (max - min) / 2 : ((max - min) % 2 == 0 ? (max - min) / 2 : (max - min));
            int mid = min + D;

            for (int n : arr) {
                int diff = Math.abs(n - mid);
                if (diff != 0 && diff != D) {
                    out.println(-1);
                    return;
                }
            }
            out.print(D);

        }

    }
}

