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.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class TaskB {
    private static final String filenameIn = "input.txt";
    private static final String filenameOut = "output.txt";

    // THIS IS SOLUTION!!!!!!!
    // LOOK HERE!
    // HACK ME PLEASE, if you can!!!


    void solve() {
        int n = nextInt();
        int[] a = nextIntArray(n);
        Set<Integer> set = new HashSet<>();
        int min = Integer.MAX_VALUE;
        int max = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            set.add(a[i]);
            max = Math.max(max, a[i]);
            min = Math.min(min, a[i]);
        }

        if (set.size() > 3) {
            out.print(-1);
            return;
        }
        if (set.size() <= 2) {
            if ((max - min) % 2 == 0) {
                out.print((max - min) / 2);
            } else {
                out.print(max - min);
            }
            return;
        }

        if ((max - min) % 2 == 0) {
            int d = (max - min) / 2;
            if (set.contains(min + d)) {
                out.print((max - min) / 2);
                return;
            }
        }
        out.print(-1);
    }


    /**
     * ШАБЛОН
     */

    public static void main(String[] args) {
        new TaskB().run();
    }

    void init() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

    void run() {
        try {
            long timeStart = System.currentTimeMillis();

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeStart));
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    /**
     * FAST_SCANNER
     */

    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st;

    String nextLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }

    private String delimiter = " ";

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        return st.nextToken(delimiter);
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[][] nextIntMatrix(int n, int m) {
        int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = nextIntArray(m);
        }
        return a;
    }

    int getMaxArray(int[] a) {
        int max = Integer.MIN_VALUE;
        for (int x : a) {
            max = Math.max(max, x);
        }
        return max;
    }

    private void setDelimiter(String delimiter) {
        this.delimiter = delimiter;
    }

}
