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.*;

/**
 * taskB
 */


public class taskB {

    public static int abstwo(ArrayList array , int i , int j) {
        return Math.abs((int)array.get(i) - (int)array.get(j));
    }

    public static boolean contains( ArrayList array,  int key) {
        for ( int i = 0 ; i < array.size() ; i++) {
            if ((int)array.get(i) == key) {
                return true;
            }
        }
        return false;
    }

    public static void main(String[] args) {
        Scanner sr = new Scanner(System.in);
        int n = sr.nextInt();
        
        ArrayList<Integer> val = new ArrayList<Integer>();
        val.add(sr.nextInt());
        int test = 0;
        int count = 1;
        for (int i = 1; i < n; i++) {
            test = sr.nextInt();
            if (!contains(val , test)) {
                val.add(test);
                count++;
            }
        }
        Collections.sort(val);;
        if(n==1) System.out.print(0);
        else if(n==2) {
            if(val.size()==2 && ((int)val.get(0) != (int)val.get(1)) && ((int)val.get(0) + (int)val.get(1))%2!=1) System.out.print(abstwo(val, 0, 1)/2);
            else if(val.size()==2 && ((int)val.get(0) != (int)val.get(1)) && ((int)val.get(0) + (int)val.get(1))%2==1) System.out.print(abstwo(val, 0, 1));
            else System.out.print(0);
        }
        else{
            if(val.size() == 1)System.out.print(0);
            else if(val.size()==2 && ((int)val.get(0) != (int)val.get(1)) && ((int)val.get(0) + (int)val.get(1))%2!=1) System.out.print(abstwo(val, 0, 1)/2);
            else { 
                
            int pace = abstwo(val, 0, 1);
            int min = (int)val.get(0);
            int max = (int)val.get(0);
            for (int i = 1; i < count; i++) {
                if((int)val.get(i) >= max) max = (int)val.get(i);
                if((int)val.get(i) <= min) min = (int)val.get(i);
            }
            boolean cond = (max - min)==(2*pace);

            boolean flag = true;
            for (int i = 1; i < count-1; i++) {
                if(!(cond && (abstwo(val, i, i+1) == pace))){ 
                    flag = false; 
                    break;
                } 
            }
            if(flag) {
                boolean condition = val.size()==2 && (Math.max((int)val.get(0),(int)val.get(1)) % Math.min((int)val.get(0),(int)val.get(1))==0) && Math.max((int)val.get(0),(int)val.get(1))!=1 && Math.min((int)val.get(0),(int)val.get(1))!= 1;
                if(condition) System.out.print(pace/2);
                else System.out.print(pace);
            }
            else System.out.print(-1);
            }
        }
        sr.close();   
    }
}