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.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(new InputStreamReader(System.in));
        int size = scanner.nextInt();
        ArrayList<Integer> nums = new ArrayList<>(size);

        for (int i = 0; i < size; i++) {
            nums.add(scanner.nextInt());
        }

        nums.sort(Integer::compareTo);

        Set<Integer> numSet = new HashSet<>(nums);
        ArrayList<Integer> numArray = new ArrayList<>(numSet);
        numArray.sort(Integer::compareTo);

        if (numArray.size() > 3){
            System.out.println(-1);
        }else if(numArray.size() == 3){
            int x1 = numArray.get(0);
            int x2 = numArray.get(1);
            int x3 = numArray.get(2);
            if (x2 - x1 == x3 - x2){
                System.out.println(x2 - x1);
            }else{
                System.out.println(-1);
            }
        }else if(numArray.size() == 2){
            int diff = numArray.get(1) - numArray.get(0);
            if (diff % 2 == 0){
                System.out.println(diff / 2);
            }else{
                System.out.println(diff);
            }
        }else if(numArray.size() == 1){
            System.out.println(0);
        }
    }
}
