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.Scanner;

/**
 * Created by suren on 4/16/19.
 */
public class TestB {
    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int n;
        n = scanner.nextInt();
        int[] a = new int[n];

        for (int i = 0 ; i < n; i++) {
            a[i] = scanner.nextInt();
        }
        D:
        for(int d = 0; d <= 100; d++) {

            int max = a[0] + d;
            int min = a[0] - d;
            int mid = a[0];
            boolean canBeMax = true;
            boolean canBeMin = true;
            boolean canBeMid = true;

            for (int i = 1 ; i < n; i++) {
                if(canBeMax) {
                    if (a[i] + d != max && a[i] - d != max && a[i] != max) {
                        canBeMax = false;
                    }
                }
                if(canBeMin) {
                    if (a[i] + d != min && a[i] - d != min && a[i] != min) {
                        canBeMin = false;
                    }
                }
                if(canBeMid) {
                    if (a[i] + d != mid && a[i] - d != mid && a[i] != mid) {
                        canBeMid = false;
                    }
                }
                if ((canBeMax || canBeMid || canBeMin) == false) {
                    continue D;
                }

            }
            if (canBeMax || canBeMid || canBeMin) {
                System.out.println(d);
                scanner.close();
                return;
            }
        }
        System.out.println(-1);
        scanner.close();
    }
}
