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.util.*;
import java.io.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class B {

    public static void main(String[] args) throws Exception {
        FastScanner scanner = new FastScanner();
        int n = scanner.nextInt();
        ArrayList<Integer> a = scanner.nextIntegerArrayList();
        Collections.sort(a);
        int step = 0;
        int target = 0;
        int i;

        for (i = 0; i < a.size() - 1; i++) {
            if (a.get(i) < a.get(i + 1)) {
                step = a.get(i + 1) - a.get(i);
                target = a.get(i + 1);
                break;
            }
        }
        if (step == 0) {
            System.out.println(step);
            System.exit(0);
        }

        boolean error1 = false;
        for (int j = i + 1; j < a.size(); j++) {
            if (a.get(j) != target && a.get(j) != target + step) {
                error1 = true;
                break;
            }
        }

        boolean error2 = false;
        if (error1 && step % 2 != 0)
            error2 = true;
        if (step % 2 == 0) {
            step /= 2;
            target -= step;
            for (int j = i + 1; j < a.size(); j++) {
                if (a.get(j) != target && a.get(j) != target + step) {
                    error2 = true;
                }
            }
        }
        if (error2)
            step *= 2;
        if (!(error1 && error2))
            System.out.println(step);
        else
            System.out.println(-1);

    }

    private static class FastScanner {
        private BufferedReader br;

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

        public int nextInt() throws IOException { return Integer.parseInt(br.readLine()); }

        public ArrayList<Integer> nextIntegerArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Integer> array = new ArrayList<Integer>();
            for (int i = 0; i < strings.length; i++)
                array.add(Integer.parseInt(strings[i]));
            return array;
        }
    }
}
