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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String []args)
    {
        Scanner scanner=new Scanner(System.in);
        int length=scanner.nextInt();
        int []array=new int[length];
        for (int i=0;i<length;++i)
        {
            array[i]=scanner.nextInt();
        }
        List<Integer> list=new ArrayList<>();
        int answer=0;
        for (int i=0; i<length;++i)
        {
            if (list.contains(array[i])== false )
            {
                list.add(array[i]);
                if (list.size()>3)
                    answer=-1;
            }

        }
        if (answer==-1 || list.size()==1)
            System.out.println(answer);
        else
        {
            if (list.size()==2)
            {
                if (Math.abs(list.get(0)-list.get(1)) %2 ==1)
                    System.out.println(Math.abs(list.get(0)-list.get(1)));
                else
                    System.out.println(Math.abs(list.get(0)-list.get(1))/2);
            }
            else
            {
                int a=list.get(0),b=list.get(1),c=list.get(2);
                if ((a-b)*(a-c)<0)
                {
                    if (Math.abs(a-b)==Math.abs(a-c))
                        System.out.println(Math.abs(a-b));
                    else
                        System.out.println(-1);
                }
                else if((b-a)*(b-c)<0)
                {
                    if (Math.abs(a-b)==Math.abs(b-c))
                        System.out.println(Math.abs(a-b));
                    else
                        System.out.println(-1);
                }
                else
                {
                    if (Math.abs(c-a)==Math.abs(b-c))
                        System.out.println(Math.abs(c-b));
                    else
                        System.out.println(-1);

                }

            }
        }

    }


}
