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.io.*;
import java.util.*;
public class Solution{

     public static void main(String []args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringTokenizer token = new StringTokenizer(br.readLine()," ");
        int a[] = new int[t];
        for(int i=0;i<t;i++){
            a[i] = Integer.parseInt(token.nextToken());
        }
        boolean b1 = false;
        boolean b2 = false;
        boolean b3 = false;
        for(int i=0;i<=100;i++){
            b1 = false;
            b2 = false;
            b3 = false;
            int x1 = a[0]+i;
            for(int j=1;j<t;j++){
                int x2 = a[j]+i;
                int x3 = a[j]-i;
                int x4 = a[j];
                if(x2 != x1 && x3 != x1 && x4 != x1){
                    b1 = true;
                    break;
                }
            }
                if(b1){
                x1 = a[0]-i;
                for(int j=1;j<t;j++){
                int x2 = a[j]+i;
                int x3 = a[j]-i;
                int x4 = a[j];
                if(x2 != x1 && x3 != x1 && x4 != x1){
                    b2 = true;
                    break;
                }
            }
            
                if(b2){
                x1 = a[0];
                for(int j=1;j<t;j++){
                int x2 = a[j]+i;
                int x3 = a[j]-i;
                int x4 = a[j];
                if(x2 != x1 && x3 != x1 && x4 != x1){
                    b3 = true;
                    break;
                }
            }
                }
                }
            if(!b1 || !b2 || !b3){
                System.out.println(i);
                break;
            }
        }
        if(b1 && b2 && b3){
            System.out.println("-1");
        }
        br.close();
     }
}