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.*;
import java.io.*;
public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int[] arr = new int[n];
		int min = 200;
		int max = -1;
		Set<Integer> set = new HashSet<Integer>();
		for (int i = 0; i < n; ++i) {
			arr[i] = Integer.parseInt(st.nextToken());
			if (arr[i] < min) min = arr[i];
			if (arr[i] > max) max = arr[i];
			if (!set.contains(arr[i])) set.add(arr[i]);
		}
		if (set.size() == 2) {
			float dp = (max-min)/2f;
			if (dp == (int)dp) System.out.println((int)dp);
			else System.out.println(max-min);
		} else {
			float dp = (max-min)/2f;
			if (dp != (int)dp) {
				System.out.println(-1);
				return;
			}
			int d = (int)dp;
			int e = min + d;
			for (int i = 0; i < n; ++i) {
				if (arr[i] + d != e && arr[i] != e && arr[i] - d != e) {
					System.out.println(-1);
					return;
				}
			}
			System.out.println(d);
		}
	}
}
