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.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.Collections;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        BSdelaiRavnimi solver = new BSdelaiRavnimi();
        solver.solve(1, in, out);
        out.close();
    }

    static class BSdelaiRavnimi {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            List<Integer> arr = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                arr.add(in.nextInt());
            }
            Set<Integer> set = new HashSet<>(arr);
            if (set.size() > 3) {
                out.println(-1);
            } else {
                List<Integer> a = new ArrayList<>(set);
                Collections.sort(a);
                if (a.size() == 1) {
                    out.println(0);
                    return;
                }
                int num = (a.get(a.size() - 1) + a.get(0)) / 2 - a.get(0);
                if (a.size() == 2) {
                    if (a.get(0) + num != a.get(1) - num) {
                        out.println(a.get(1) - a.get(0));
                        return;
                    } else {
                        out.println(num);
                        return;
                    }
                } else {
                    int mid = a.get(0) + num;
                    for (int nn : a) {
                        if (nn != mid && nn + num != mid && nn - num != mid) {
                            out.println(-1);
                            return;
                        }
                    }
                    out.println(num);
                }

            }
        }

    }
}

