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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] arr =new int[n];
		for(int i = 0; i < n ; i++){
			arr[i] = scan.nextInt();
		}
		for(int i = 0;i<=100;i++){
			for(int j = 0 ; j < n ; j++){
				int one = arr[j]+i;
				int two = arr[j]-i;
				int three = arr[j];
				boolean check = true;
				for(int k = 0; k < n ; k++){
					if(k == j)continue;
					if(arr[k] > one){
						int now = arr[k]-i;
						if(now != one){
							check = false;
							break;
						}
					}
					if(arr[k] < one){
						int now = arr[k]+i;
						if(now != one){
							check = false;
							break;
						}
					}
				}
				if(check){
					System.out.println(i);
					return;
				}
				check = true;
				for(int k = 0 ; k < n ; k++){
					if(k == j)continue;
					if(arr[k] > two){
						int now = arr[k]-i;
						if(now != two){
							check = false;
							break;
						}
					}
					if(arr[k] < two){
						int now = arr[k]+i;
						if(now != two){
							check = false;
							break;
						}
					}
				}
				if(check){
					System.out.println(i);
					return;
				}
				check = true;
				for(int k = 0 ; k < n ; k++){
					if(k == j)continue;
					if(arr[k] > three){
						int now = arr[k]-i;
						if(now != three){
							check = false;
							break;
						}
					}
					if(arr[k] < three){
						int now = arr[k]+i;
						if(now!=three){
							check = false;
							break;
						}
					}
				}
				if(check){
					System.out.println(i);
					return;
				}
			}
			
		}
		System.out.println(-1);
	}}