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 Codeforces {
   static boolean check(int arr[],int d,int val)
   {
       for(int j=1;j<arr.length;j++)
       {
           if(arr[j]==val)
               continue;
           else if(arr[j]+d==val)
               continue;
           else if(arr[j]-d==val)
               continue;
           else
               return false;
       }
       return true;
   }
    public static void main(String[] args) throws java.lang.Exception {
        /* your code goes here */
        BufferedReader buf = new BufferedReader(new InputStreamReader(System.in));
       //int t = Integer.parseInt(buf.readLine());
        StringBuilder sb = new StringBuilder();

       // for (int i = 0; i < t; i++) {
            String st1[] = (buf.readLine()).split(" ");
            int n=Integer.parseInt(st1[0]);
            int arr[]=new int[n];
            String st2[]=(buf.readLine()).split(" ");
            for(int j=0;j<n;j++)
                arr[j]=Integer.parseInt(st2[j]);
            int flag=0;
            if(n==1)
                sb.append(0);
            else {
                for (int d = 0; d <= 100; d++) {
                    int val1 = arr[0] + d;
                    int val2 = arr[0] - d;
                    int val3 = arr[0];
                    if(check(arr,d,val1)==true)
                    {
                        sb.append(d);
                        flag=1;
                        break;
                    }
                    else if(check(arr,d,val2)==true)
                    {
                        sb.append(d);
                        flag=1;
                        break;
                    }
                    else if(check(arr,d,val3)==true)
                    {
                        sb.append(d);
                        flag=1;
                        break;
                    }
                    else
                    {
                        continue;
                    }
                }
                if(flag==0)
                    sb.append(-1);
            }
       // }
        System.out.println(sb);
    }
}