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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class MakeThemEqual {
	public static void main(String[] args) throws IOException {
		BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer stringTokenizer = new StringTokenizer(bufferedReader.readLine());
		int n = Integer.parseInt(stringTokenizer.nextToken());
		ArrayList<Integer> list = new ArrayList<>();
		stringTokenizer = new StringTokenizer(bufferedReader.readLine());
		Map<Integer,Integer> map = new HashMap<>();
		for (int i = 0; i < n; i++) {
			int x = Integer.parseInt(stringTokenizer.nextToken());
			if (map.get(x) == null) {
				list.add(x);
				map.put(x, 1);
			}
		}
		Collections.sort(list);
		if (list.size() == 1) {
			System.out.println(0);
		}else if(list.size() == 2 && (list.get(1) - list.get(0)) % 2 == 0) {
			System.out.println((list.get(1) - list.get(0)) / 2 );
		} else if (list.size() > 3) {
			System.out.println(-1);
		} else {
			int d = list.get(1) - list.get(0);
			int flag = 0;
			for (int i = 1; i < list.size(); i++) {
				if (list.get(i) - list.get(i - 1) != d) {
					flag++;
				}
			}
			if (flag == 0) {
				System.out.println(d);
			} else {
				System.out.println(-1);
			}
		}
	}
}
