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 Program {

    static int[] inputs;

    public static void main(String[] args){
        final MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        inputs = new int[n];
        for (int i = 0; i < n; i++){
            inputs[i] = sc.nextInt();
        }

        System.out.println(calculate());
    }

    public static Integer calculate(){
        TreeMap<Integer, Boolean> values = new TreeMap<>();
        for (Integer value: inputs) {
            if (!values.containsKey(value)){
                values.put(value, true);
            }
        }

        if (values.size() == 1){
            return 0;
        }

        if (values.size() >= 4) {
            return -1;
        }

        if (values.size() == 2) {
            int diff = values.pollLastEntry().getKey() - values.pollFirstEntry().getKey();
            if (diff % 2 == 0){
                return diff / 2;
            }
            return diff;
        }

        if (values.size() == 3){
            int min = values.pollFirstEntry().getKey();
            int max = values.pollLastEntry().getKey();
            int middle = values.pollFirstEntry().getKey();
            if (max - middle == middle - min){
                return max - middle;
            }
        }

        return -1;
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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());
        }

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

    }
}