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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	 Scanner sc=new Scanner(System.in);
	 int n=sc.nextInt();
	 ArrayList<Integer> al=new ArrayList<>();
	 TreeSet<Integer> st=new TreeSet<>();
	 
	 for(int i=0;i<n;i++)
	 {
	     int a=sc.nextInt();
	     al.add(a);
	     st.add(a);
	 }
	 Collections.sort(al);
	 int max=al.get(n-1);
	 int min=al.get(0);
	 int c=0;
	 if(st.size()>1)
	 {
	 while(al.contains(max))
	  al.remove(al.get(al.size()-1));
	 while(al.contains(min))
	  al.remove(al.get(0));
	 }
//	 System.out.println(al);
	 if((max-min)%2==0)
	 {
	      c=(max-min)/2;
	 }
	 else
	   c=max-min;
	 if(st.size()>3)
	   c=-1;
	 if(al.contains(max-c) || al.contains(min+c) || (st.size()==2 && (max-c==min+c || max-c==min)))
	  System.out.println(c);
	 else
	  System.out.println(-1);
	}
}
