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 asdasdasdasd {
	public static boolean two(int ar[])
	{
		int one=ar[0];int two=ar[ar.length-1];
		for(int i=0;i<ar.length;i++)
		{
			if(ar[i]==one || ar[i]==two)
			{
				
			}else {
				return false;
			}
		}
		return true;
	}
	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int ar[]=new int[n];
		for(int i=0;i<n;i++)
		{
			ar[i]=scan.nextInt();
		}
		Arrays.parallelSort(ar);
		int need=ar[n-1]-ar[0];
		int cost=0;
		if(need%2==0)
		{
			need=need/2;
			for(int i=0;i<n;i++)
			{
				if(ar[i]!=ar[0] && ar[i]!=ar[n-1]&& (ar[i]!=(ar[0]+need))&&(ar[i]!=(ar[n-1]-need)))
				{
					System.out.println(-1);
//					brea
					return;
				}
				if(ar[i]!=(ar[0]+need)&& (ar[i]!=ar[n-1]-need))
				{
					cost++;
				}
			}
			System.out.println(need);
		}else {
			if(two(ar))
			{
				System.out.println(ar[n-1]-ar[0]);
			}else {
			System.out.println(-1);
			}
			}
		
	}
}
