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.io.*;
import java.util.*;
public class Main
{
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int a[]=new int[n];
		HashSet<Integer> hs=new HashSet<>();
		for( int i=0;i<n;i++)
		{
		     a[i]=sc.nextInt();
		     hs.add(a[i]);
		     
		}
		List<Integer> l = new ArrayList<>(hs); 
        Collections.sort(l); 
		if(hs.size()==1)
		{
		     System.out.println(0);
		     System.exit(0);
		}
		if(hs.size()==2)
		{
		     if((((l.get(0)%2)!=0)&&(l.get(1)%2)!=0)||(((l.get(0)%2)==0)&&((l.get(1)%2)==0)))
		     {
		          System.out.println(((l.get(0)+l.get(1))/2)-l.get(0));
		          System.exit(0);
		     }
		     else
		     {
		          System.out.println(l.get(1)-l.get(0));
		          System.exit(0);
		     }
		}
		if(hs.size()==3)
		{
		     int x=l.get(1)-l.get(0);
		     int y=l.get(1)+x;
		     if((y==l.get(2)))
		     {
		          System.out.println(x);
		               System.exit(0);
		     }
		       
		  }
		  
		  System.out.println(-1);
		}
	}
