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.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] arr = new int[n];
        for (int i=0;i<n;i++){
            arr[i] = scanner.nextInt();
        }
        //sort method
        arr = sort(arr);
        //find D
        System.out.println(findD(arr));
    }

    static int[] sort(int[] arr){
        for (int item:arr){
            for (int i=0;i<arr.length-1;i++){
                if (arr[i]>arr[i+1]){
                    int tmp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = tmp;
                }
            }
        }
        return arr;
    }

    static int findD(int[] arr){
        int D = 0;
        int count = 0;
        boolean flag = true;
        for (int i =0 ;i<arr.length-1;i++){
            if (arr[i]!=arr[i+1]){
                int tmp = arr[i+1] - arr[i];
                if (flag){
                    D = tmp;
                    count++;
                    flag = false;
                }else {
                    if (tmp!=D || count>=2){
                        D = -1;
                        break;
                    }
                    count++;
                }
            }
        }
        if (D%2==0 && count<2)
            D/=2;
        return D;
    }
}
