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.*;

/**
 * @Author: Harry
 * @Date: 2019-04-19 21:37
 * @Version 1.0
 */
public class Main {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);


        while (input.hasNext()){
            int n = input.nextInt();

            int arr[] = new int[n];

            Set<Integer> s = new HashSet<Integer>();

            for(int i = 0;i < n;i++){
                arr[i] = input.nextInt();
                s.add(arr[i]);
            }

            if(n == 1 || s.size() == 1){
                System.out.println(0);
                continue;
            }

            int tp[] = new int[s.size()];
            Set<Integer> check = new HashSet<Integer>();

            int counter = 0;
            for(int x:s){
                tp[counter++] = x;
            }


            Arrays.sort(tp);

            for(int i = 1;i < tp.length;i++){
                check.add(tp[i] - tp[i - 1]);
                if(((tp[i] - tp[i - 1]) & 1) != 1)
                    check.add((tp[i] - tp[i - 1]) / 2);
                //System.out.println(tp[i] - tp[i - 1]);
            }


            int d = 999999999;

            for(int dd:check){
                Map<Integer,Integer> map = new HashMap<Integer,Integer>();
                //System.out.println("dd:" + dd);
                for(int x:arr){
                    int a = x + dd;
                    int b = x - dd;
                    int c = x;

                    //System.out.println(a + " " + b + " " + c);

                    cal(a,map);
                    cal(b,map);
                    cal(c,map);
                }

                for(Map.Entry<Integer,Integer> entry:map.entrySet()){
                    if(entry.getValue() == n){
                        d = Math.min(d,dd);
                    }
                }
            }


            if(d == 999999999){
                System.out.println(-1);
            }
            else{
                System.out.println(d);
            }
        }

    }


    public static void cal(int a,Map<Integer,Integer> map){
        if(map.containsKey(a)){
            map.put(a,map.get(a) + 1);
        }
        else{
            map.put(a,1);
        }
    }



}
