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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class MakeThemEqual {

    public static void main(String[] args) {
        Scanner scanner = new Scanner();

        int n = scanner.nextInt();
        Set<Integer> set = new HashSet<>();
        List<Integer> unique = new ArrayList<>();

        for(int i=0; i<n; i++) {
            int val = scanner.nextInt();
            if(!set.contains(val)) {
                unique.add(val);
                set.add(val);
            }
        }

        Collections.sort(unique);

        if(unique.size() > 3) {
            System.out.println("-1");

        } else if(unique.size() == 3) {
            int v1 = unique.get(0);
            int v2 = unique.get(1);
            int v3 = unique.get(2);

            if(v2 - v1 == v3 - v2)
                System.out.println(v2-v1);
            else
                System.out.println("-1");

        } else if(unique.size() == 2) {
            int v1 = unique.get(0);
            int v2 = unique.get(1);

            if((v1+v2) % 2 != 0)
                System.out.println(v2-v1);
            else
                System.out.println((v1+v2)/2 - v1);

        } else {
            System.out.println(0);
        }
    }

    private static class Scanner {
        private BufferedReader br;
        private StringTokenizer st;

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

        String next() {
            if(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;
        }
    }
}

