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.*;


public class Main {
	
	static int Maxn=105;
	
	
	
	public static void main(String arg[]){
		
		Set<Integer>s=new TreeSet<>();
		Scanner cin=new Scanner(System.in);
		int n=cin.nextInt();
		int a[]=new int[n];
		
		
		for(int i=0;i<n;i++){
			a[i]=cin.nextInt();
			s.add(a[i]);
		}
	
		
		if(s.size()==1){
			System.out.println(0);
		}else if(s.size()==2){
			
			
			Arrays.sort(a);
	
			int tt=a[n-1]-a[0];
			if(tt%2==0)System.out.println(tt/2);
			else System.out.println(tt);
			
			
		}else if(s.size()==3){
			int b[]=new int[Maxn];
			int cnt=0;
			for(Integer value:s){
				b[cnt++]=value;
			}
			
			int temp=b[1]-b[0];
			int flag=0;
			for(int i=1;i<cnt-1;i++){
				if(b[i+1]-b[i]!=temp){
					flag=1;
					break;
				}
			}
			if(flag==1){
				System.out.println(-1);
			}else{
				System.out.println(temp);
				
			}
		}else{
			System.out.println(-1);
		}
		cin.close();
	}
	

}
