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.*;
public class a {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int[] arr = new int[n];
    for (int i = 0; i  < n; i++)
        arr[i] = in.nextInt();
        Arrays.sort(arr);
        int a =-1, b = -1, c = -1;
        for (int i = 0; i < n;i++) {
            if (a == arr[i] ||  a== -1) a = arr[i];
            else if (b == arr[i] ||  b== -1) b = arr[i];
            else if (c == arr[i] ||  c== -1) c = arr[i];
            else {
                System.out.println(-1);
                return;
            }
            
            
            
        }
if (b == -1 ) System.out.println(0);
else        if (c != -1 && c - b != b - a) System.out.println(-1);
        else if (c == -1 &&(b-a) %2 == 0)System.out.println((b-a)/2); else System.out.println(b-a);
    }
}