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.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {
    private static final fast sc = new fast();
    private static final BufferedWriter sout = new BufferedWriter(new OutputStreamWriter(System.out));
    private static final int OO = (int) 2e5 + 1;
    private static final double PI = 3.141592653;
    private static final int[] dx4 = {0, 1, 0, -1}, dx = {0, 0, 1, -1, 1, -1, 1, -1};
    private static final int[] dy4 = {1, 0, -1, 0}, dy = {1, -1, 0, 0, 1, -1, -1, 1};
    //static void print6P{ System.out.printf("%8.6f\n"); }

    public static void main(String[] args) throws IOException {
        int n = sc.nextInt();
        int[] arr = new int[n], fre = new int[101];
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
            if (fre[arr[i]] == 0) {
                list.add(arr[i]);
            }
            fre[arr[i]] += 1;
        }
        Collections.sort(list);
        if (list.size() == 1) {
            sout.write(0 + "");
        } else if (list.size() == 2) {
            int dif = list.get(1) - list.get(0);
            sout.write(((dif % 2 == 0) ? dif / 2 : dif) + "");
        } else if (list.size() == 3) {
            double s = 0;
            for (Integer integer : list) {
                s += integer;
            }
            s /= list.size();
            int a = (int) (list.get(list.size() - 1) - s);
            for (int i = 0; i < list.size(); i++) {
                if (list.get(i) > s) {
                    list.set(i, list.get(i) - a);
                } else if (list.get(i) < s) {
                    list.set(i, list.get(i) + a);
                }
            }
            if (isE(list)) {
                sout.write(a + "");
            } else {
                sout.write(-1 + "");
            }
        } else {
            sout.write(-1 + "");
        }
        sout.close();
    }

    static boolean isE(ArrayList<Integer> list) {
        for (int i = 0; i < list.size() - 1; i++) {
            if (!list.get(i).equals(list.get(i + 1))) {
                return false;
            }
        }
        return true;
    }

    static class fast {
        BufferedReader br;
        StringTokenizer st;

        public fast() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }


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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double nextFloat() {
            return Float.parseFloat(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static class Pair implements Comparable<Pair> {
        int first;
        int second;

        Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public int compareTo(Pair o) {
            return Double.compare(o.first, first);
        }
    }
}

