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
// Name: Jeffrey Bindeman
// Date:
// Description

import java.io.*;
import java.util.*;

public class Main {

	public static Scanner in = new Scanner(System.in);

	public static void main(String[] args) {

		int n = in.nextInt(), x, min = Integer.MAX_VALUE, max = Integer.MIN_VALUE, int1, int2;
		HashSet<Integer> set = new HashSet<>();
		ArrayList<Integer> first = new ArrayList<>();

		for (int i = 0; i < n; i++) {
			x = in.nextInt();
			if (x < min) {
				min = x;
			}
			if (x > max) {
				max = x;
			}
			set.add(x);
		}

		double mid = (max - min);
		
		if (set.size() == 2) {
			if (mid %2 == 0){
				System.out.println((int) (mid/2));
			}
			else{
				System.out.println((int) mid);
			}
			
			return;
		}
		
		
		first.add(min - ((int) mid));
		first.add(min);
		first.add(min + ((int) mid));

		if (mid % 2 != 0) {
			System.out.println("-1");
			return;
		}

		mid /= 2;

		for (int i : set) {
			int1 = i + ((int) mid);
			int2 = i - ((int) mid);
			if (!first.contains(i) && !first.contains(int1) && !first.contains(int2)) {
				System.out.println("-1");
				return;
			}
		}

		System.out.println((int) mid);
	}
}
