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 Test1 {

    
    public static void main(String[] args) {
        Scanner in =new Scanner(System.in);
        HashSet<Integer> set=new HashSet<Integer>();
        int n=in.nextInt();
        int[]z=new int[n];
        for(int i=0;i<n;i++){
            z[i]=in.nextInt();
            set.add(z[i]);
        }
       
        if(set.size()>3)
            System.out.println(-1);
        else{
            if(set.size()==1)
                System.out.println(0);
            else if(set.size()==2){
                int a=z[0];
                int b=-1;
                int tmp1=a;
                
                for(int i=0;i<n;i++)
                    if(z[i]!=a)
                        b=z[i];
                int tmp2=b;
               
                a=Math.max(tmp1,tmp2);
                b=Math.min(tmp1,tmp2);
               
                if((a-b)%2==0)
                    System.out.println((a-b)/2);
                else
                    System.out.println(a-b);
            }
            else{
             
                int a=z[0];
                int b=-1;
                int c=-1;
                int[]x={0,0,0};
                Iterator ptr=set.iterator();
                a=(int) ptr.next();
                b=(int) ptr.next();
                c=(int) ptr.next();
                x[0]=a;x[1]=b;x[2]=c;
                Arrays.sort(x);
                a=x[0];b=x[1];c=x[2];
                if ((c - a) % 2 == 0)
		{
			if (a + (c - a) / 2 == b)
                            System.out.println((c - a) / 2);
                        else
                            System.out.println(-1);
		}
		else
                    System.out.println(-1);
            }
           
        }
    }
    
}
