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 Main {


    public static void main(String[] args) {
        FastReader f = new FastReader();

        int n = f.nextInt();

        int[] arr = new int[3];

        while (n-- > 0) {
            int loc = f.nextInt();

            if(arr[0] == 0 || arr[0] == loc) {
                arr[0] = loc;
            } else if(arr[1] == 0 || arr[1] == loc) {
                arr[1] = loc;
            } else if(arr[2] == 0 || arr[2] == loc) {
                arr[2] = loc;
            } else {
                System.out.println(-1);
                return;
            }
        }

        int cnt = 0;
        for(int i : arr) {
            if(i != 0) {
                cnt++;
            }
        }

        //System.out.println(cnt);
        if(cnt == 1) {
            System.out.println(0);
            return;
        }

        if(cnt == 2) {
            if(arr[0] % 2 == arr[1] % 2) {
                System.out.println(Math.abs(arr[0]-arr[1])/2);
            } else {
                System.out.println(Math.abs(arr[0]-arr[1]));
            }
            return;
        }

        Arrays.sort(arr);

        if(arr[1] - arr[0] != arr[2] - arr[1]) {
            System.out.println(-1);
            return;
        }

        System.out.println(arr[1] - arr[0]);

    }








    //fast input reader
    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 str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}


