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
/* package whatever; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner in = new Scanner(System.in);
		in.nextLine();
		String[] arr1 = in.nextLine().split(" ", -1);
		arr1 = Arrays.stream(arr1).distinct().toArray(String[]::new);
		int[] arr2 = Arrays.stream(arr1).mapToInt(Integer::parseInt).toArray();;
		Arrays.sort(arr2);
		
		int result = -2;
		if(arr2.length > 3)result=-1;
		if(arr2.length == 1)result=0;
		if(arr2.length == 2){
			result=arr2[1]-arr2[0];
			if( (arr2[1]-arr2[0]) %2 == 0){
				result/=2;
			}
		}
		if(arr2.length == 3){
			if( (arr2[2]-arr2[1]) == (arr2[1]-arr2[0]) ){
				result=arr2[2]-arr2[1];
			}else{
				result=-1;
			}
		}
		
		System.out.println(result);
	}
}
	 	 	  	   				 				  	  						