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;
import java.util.SortedSet;
import java.util.TreeSet;

public class P_1154B {

	public static final String NAME = "Make Them Equal";
	
	public static void main(String[] args) {
		
		try (Scanner sc = new Scanner(System.in)) {
			
			int n = sc.nextInt();
			SortedSet<Integer> numbers = new TreeSet<>();
			
			for (int i = 0; i < n; i++) {
				numbers.add(sc.nextInt());
			}
			List<Integer> list = new ArrayList<>(numbers);
			
			if (3<list.size()) System.out.println("-1");
			else if (list.size()==3) {
				if (list.get(2)-list.get(1)!=list.get(1)-list.get(0)) System.out.println("-1");
				else System.out.println(list.get(1)-list.get(0));
			}
			else if (list.size()==2) {
				if ((list.get(1)-list.get(0))%2==0) System.out.println((list.get(1)-list.get(0))/2);
				else System.out.println((list.get(1)-list.get(0)));
			}
			else System.out.println("0");
		}
		catch (Exception e) {
			e.printStackTrace();
		}
	}
}