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 //do not write package name here */

import java.io.*;
import java.util.*;
public class S {
	public static void main (String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int a[]=new int[n];
		int max=Integer.MIN_VALUE,min=Integer.MAX_VALUE;
		Set<Integer> set=new HashSet<>();
		for(int i=0;i<n;i++)
		{
		    a[i]=in.nextInt();
		    set.add(a[i]);
		    if(max<a[i])max=a[i];
		    if(min>a[i])min=a[i];
		}
		
		if(set.size()>3)System.out.print(-1);
		else if(set.size()==1)
		{
		    System.out.print(0);
		}
		else if(set.size()==3)
		{
		    ArrayList<Integer> al=new ArrayList<>(set);
		    Collections.sort(al);
		    if((al.get(1)-al.get(0))==(al.get(2)-al.get(1)))System.out.print(al.get(1)-al.get(0));
		    else System.out.print(-1);
		}
		else if(set.size()==2)
		{
		    int d=max-min;
		    if(d%2==0)System.out.print(d/2);
		    else System.out.print(d);
		}
	}
}