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.*;

public class Comp implements Closeable {
    static String filePath = "/home/bishoy/IdeaProjects/Arabic competetive programming/src/b/test";
    BufferedReader inputReader = new Helper().readInput(Helper.STD, filePath);
    PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String args[]) throws Exception {
        Comp comp = new Comp();
        int t = 1;
        while (t-- > 0) {
            comp.solve2();
        }
        comp.close();

    }


    public void solve2() throws IOException {

        int n = nextInt();
        Set<Integer> set = new HashSet<>();
        for (int i = 0; i < n; i++) {
            set.add(nextInt());
            if (set.size() > 3) {
                writer.println(-1);
                return;
            }
        }


        int ans = 0;
        ArrayList<Integer> list = new ArrayList<>(set);
        if (set.size() > 3) {
            ans = -1;
        } else if (set.size() <= 2) {
            if (set.size() == 1)
                ans = 0;
            else {
                ans = (Math.abs(list.get(0) - list.get(1)));
                if (ans % 2 == 0)
                    ans /= 2;
            }

        } else {

            Collections.sort(list);
            if (list.get(2) - list.get(1) == list.get(1) - list.get(0))
                ans = list.get(1) - list.get(0);
            else
                ans = -1;
        }

        writer.println(ans);
    }

    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(inputReader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

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

    static class Helper {
        BufferedReader inputReader = null;
        PrintWriter out = null;
        public static final int FILE = 0;
        public static final int STD = 1;

        public static class Pair<K, V> {
            public K key;
            public V value;

            public Pair(K key, V value) {
                this.key = key;
                this.value = value;
            }


            @Override
            public String toString() {
                return "( " + key + " , " + value + ")";
            }
        }


        public BufferedReader readInput(int type, String filePath) {
            if (type == FILE) {
                try {
                    inputReader = new BufferedReader(
                            new InputStreamReader(new FileInputStream(filePath)));
                } catch (FileNotFoundException e) {
                    e.printStackTrace();
                }
            } else
                inputReader = new BufferedReader(new InputStreamReader(System.in));


            return inputReader;
        }

    }
}