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.Arrays;
import java.util.StringTokenizer;

/**
 *
 * @author Haya
 */
public class MakeThemEqual {

    public static void main(String[] args) {
        
        FastReader in = new FastReader();
        
        int n = in.nextInt();
        int[] array = new int[n];
        int max = 0, min = 101;
 
        for (int i = 0; i < n; i++) {
            array[i] = in.nextInt();
            max = Math.max(max, array[i]);
            min = Math.min(min, array[i]);
        }
        int ans = check(array, min);
        int avg = (max + min) /2;
        int res = check(array, avg);
 
        if (res != -1) {
            if (ans == -1 || res < ans)
                ans = res;
        }
 
        System.out.println(ans);
    
            
    }
    
    public static int check(int[] array, int num) {
        int res = 0;
        for (int i = 0; i < array.length; i++) {
            if (array[i] != num) {
                if (res == 0)
                    res = Math.abs(array[i] - num);
                else if (res != Math.abs(array[i] - num))
                    return -1;
            }
        }
        return res;
        
    }

    public static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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 string = "";
            try {
                string = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return string;
        }

    }

}
