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 B1
{
    public static void main(String ar[])
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
        }
        Arrays.sort(a);

        int t1=1;
        int value=a[0];
        for(int i=1;i<n;i++)
        {
            if(a[i]!=value)
            {
                t1++;
                value=a[i];
            }
        }
        if(t1==1)
        {
            System.out.println(0);
            return;
        }


        if(t1==2)
        {
            if((a[n-1]-a[0])%2==0)
                System.out.println((a[n-1]-a[0])/2);
            else
                System.out.println(a[n-1]-a[0]);
            return;
        }

        for(int i=1;i<n-1;i++)
        {
            int d=Math.abs(a[i]-a[0]);
            int j=0;
            for(j=0;j<n;j++)
            {
                if(a[j]!=a[i] && Math.abs(a[j]-a[i])!=d)
                    break;
            }
            if(j==n)
            {
                System.out.println(Math.abs(a[i]-a[0]));
                return;
            }
        }
        System.out.println(-1);
    }
}