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 Main {
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok = new StringTokenizer("");
    String next() throws IOException {
        if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
        return tok.nextToken();
    }
    int nextInt() throws IOException { return Integer.parseInt(next()); }
    
    void solve() throws IOException {
        int n = nextInt();
        boolean[] a = new boolean[101];
        ArrayList<Integer> c = new ArrayList();
        for (int b=0;b<n;b++) {
            int x = nextInt();
            if (!a[x]) {
                c.add(x);
                a[x]=true;
            }
        }
        switch (c.size()) {
            case 1:
                System.out.println("0");
                break;
            case 2:
                if ((Math.abs(c.get(0)-c.get(1)))%2==0) System.out.println((Math.abs(c.get(0)-c.get(1)))/2);
                else System.out.println(Math.abs(c.get(0)-c.get(1)));
                break;
            case 3:
                Collections.sort(c);
                if (c.get(2)-c.get(1)==c.get(1)-c.get(0)) {
                    System.out.println(c.get(2)-c.get(1));
                    break;
                }
            default:
                System.out.println("-1");
                
        }
    }
    
    public static void main(String[] args) throws IOException {
        new Main().solve();
    }
}
    
