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.io.*;

/*

*/

public class Main{
    
    public static void main(String[] args) throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

        StringTokenizer st=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(st.nextToken());
        int[] arr=new int[n];
        st=new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++){
            arr[i]=Integer.parseInt(st.nextToken());
        }
        Arrays.sort(arr);
        int differ=0,count=0;
        int flag=0;
        for(int i=1;i<n;i++){
            int diff=arr[i]-arr[i-1];
            if(diff!=0){
                if(differ==0||differ==diff){
                    differ=diff;
                    count++;    
                }else{
                    flag=1;
                    break;
                }
            }
        }

        if(flag==1){
            pw.println("-1");
        }else{
            if(count==1){
                if(differ%2==0){
                    pw.println(differ/2);
                }else{
                    pw.println(differ);
                }
            }else if(count==2||count==0) {
                pw.println(differ);
            }else{
                pw.println("-1");
            }
        }
        
        
        pw.close();
    }
}
