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 pa {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws IOException {
        int n = readInt();
        int[] a = readArrayInt();

        for (int d = 0; d <= 100; d++) {
            for (int t = 0; t <= 100; t++) {
                boolean ch = false;
                for (int i = 0; i < n; i++)
                    if (!(a[i] == t || a[i] + d == t || a[i] - d == t)) {
                        ch = true;
                        break;
                    }
                if (!ch) {
                    System.out.println(d);
                    return;
                }
            }
        }
        System.out.println(-1);
    }

    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static char[] readString() throws IOException {
        return br.readLine().toCharArray();
    }

    static int[] readArrayInt() throws IOException {
        String s[] = br.readLine().split(" ");
        int a[] = new int[s.length];
        for (int i = 0; i < s.length; i++)
            a[i] = Integer.parseInt(s[i]);
        return a;
    }

    static char[][] readArrayString() throws IOException {
        String s[] = br.readLine().split(" ");
        char a[][] = new char[s.length][];
        for (int i = 0; i < s.length; i++)
            a[i] = s[i].toCharArray();
        return a;
    }

/*
    Arrays.sort(a, (char[] p1, char[] p2) -> {
                if (p1.length != p2.length)
                    return Integer.compare(p1.length, p2.length);
                return p1.toString().compareTo(p2.toString());
        });



    //Collections.sort(odd);


 for (Map.Entry<Integer, Integer> e: b.entrySet()) {
            int k = e.getKey();
            int v = e.getValue();

        }*/

}

