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.Arrays;
import java.util.Scanner;

public class TaskB {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] num = new int[n];
		for(int i=0;i<n;i++) {
			num[i] = s.nextInt();
		}
		int a=0,b=0,c=0;
		int dif=0;
		a = num[0];
		for(int i=0;i<n;i++) {
			if(num[i] != a) {
				b = num[i];
				break;
			}
		}
		for(int i=0;i<n;i++) {
			if(num[i] != a && num[i] != b) {
				c = num[i];
				break;
			}
		}
		if(b == 0) {
			System.out.println(0);
			return;
		}
		if(c == 0) {
			if(Math.abs(a-b) %2 == 0) {
				System.out.println(Math.abs(a-b)/2);
			} else {
				System.out.println(Math.abs(a-b));
			}
			return;
		}
		int[] lel = new int[] {a,b,c};
		Arrays.sort(lel);
		dif = lel[1] - lel[0];
		for(int i=0;i<n;i++) {
			if(num[i] != lel[1] && num[i] != lel[1] - dif && num[i] != lel[1] + dif) {
				System.out.println(-1);
				return;
			}
		}
		System.out.println(dif);
	}
}
