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

import static java.util.stream.Collectors.groupingBy;

public class Main {

    private interface Input extends Closeable {
        String next() throws IOException;

        default int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }

    public static class MapData {
        Map<Character, List<Integer>> myMap = new HashMap<>();

        public void add(Character character, Integer index) {
            if (!myMap.containsKey(character)) {
                List<Integer> myList = new ArrayList<>();
                myList.add(index);
                myMap.put(character, myList);
            } else {
                List<Integer> myList = myMap.get(character);
                myList.add(index);
            }
        }

        public List<Integer> getAvailableIndex() {
            return myMap.entrySet().stream().map(Map.Entry::getValue).flatMap(List::stream).collect(Collectors.toList());
        }

        public int pop(Character character) {
            if (!myMap.containsKey(character))
                return popFromQuestion();
            else {
                List<Integer> myList = myMap.get(character);
                if (myList.size() > 0)
                    return myList.remove(myList.size() - 1);
                else return popFromQuestion();
            }
        }

        private int popFromQuestion() {
            if (!myMap.containsKey('?'))
                return -1;
            else {
                List<Integer> myList = myMap.get('?');
                if (myList.size() > 0)
                    return myList.remove(myList.size() - 1);
                else return -1;
            }
        }
    }

    public static class MyObject {
        int i;
        char character;


        MyObject(int i, char j) {
            this.i = i;
            this.character = j;
        }
    }

    public static void main(String[] args) throws IOException {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        List<Integer> data = IntStream.range(0, n).boxed().map(i -> scanner.nextInt()).sorted().collect(Collectors.toList());
        int range = data.get(n - 1) - data.get(0);

        int result = IntStream.rangeClosed(0, range).boxed().filter(d -> check(data, d)).findFirst().orElse(-1);

        System.out.println(result);
    }

    private static boolean check(List<Integer> data, Integer d) {
        return (checkEqual(data, d, data.get(0)) || checkEqual(data, d, data.get(0) + d));
    }

    private static boolean checkEqual(List<Integer> data, Integer d, int value) {
        return data.stream().allMatch(currentValue -> currentValue == value || currentValue - d == value || currentValue + d == value);
    }
}