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 Solution {
	
	static int[] insertSort(int[] array) {
        for (int i = 1; i < array.length; i++) {
            int j = i - 1;
            int tmp = array[i];
            while (j >= 0 && array[j] > tmp) {
                array[j+1] = array[j];
                j--;
            }
            array[j+1] = tmp;
        }
        return array;
    }
	
	public static void main(String[] args) {
		 Scanner scanner = new Scanner(System.in);
		 
		 int n = scanner.nextInt();
		 int[] numbers = new int[3];
		 numbers[0] = scanner.nextInt();
		 int nunique = 1;
		 int a;
		 boolean unique;
		 int answer = 0;
		 
		 for (int i = 1; i < n; i++) {
			 a = scanner.nextInt();
			 unique = true;
			 for (int j = 0; j < nunique; j++) {
				 if (numbers[j] == a) {
					 unique = false;
					 break;
				 }
			 }
			 if (unique) {
				 if (nunique > 2) {
					 answer = -1;
					 break;
				 }
				 numbers[nunique] = a;
				 nunique++;
			 }
		 }
		 
		 if (answer != -1) {
			 if (nunique == 1)
				 answer = 0;
			 else if (nunique == 2) {
				 int diff;
				 if (numbers[0] > numbers[1])
					 diff = numbers[0] - numbers[1];
				 else
					 diff = numbers[1] - numbers[0];
				 if (diff % 2 == 0)
					 answer = diff / 2;
				 else
					 answer = diff;
			 } else {
				 insertSort(numbers);
				 if (numbers[2] - numbers[1] == numbers[1] - numbers[0])
					 answer = numbers[2] - numbers[1];
				 else
					 answer = -1;
				 
			 }
		 }
		 
		 System.out.println(answer);
		 	 
		 scanner.close();
		 
		 
	}
}
