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.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class p2 {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

        int n = in.nextInt();

        int[] a = new int[n];

        int[] val = new int[2];

        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }

        Arrays.sort(a);

        val[0] = a[n-1] - a[0];
        if (val[0]%2 == 0)
            val[1] = val[0]/2;
        else
            val[1] = -1;

        boolean[] test = new boolean[3];

        test[0] = true;
        test[1] = true;
        test[2] = true;

        for (int i = 0; i < n; i++) {
            if (!check(a[n-1], val[0], a[i])) {
                test[0] = false;
            }
        }

        for (int i = 0; i < n; i++) {
            if (!check(a[n-1] - val[1], val[1], a[i])) {
                test[1] = false;
            }
        }

        for (int i = 0; i < n; i++) {
            if (!check(a[0], val[0], a[i])) {
                test[2] = false;
            }
        }

        if (test[0] || test[2] && test[1]) {
            if (Math.min(val[0], val[1]) >= 0) {
                System.out.println(Math.min(val[0], val[1]));
                return;
            }
        }

        if (test[0] || test[2]) {
            System.out.println(val[0]);
        } else if (test[1]) {
            System.out.println(val[1]);
        } else {
            System.out.println("-1");
        }

    }

    public static boolean check(int target, int val, int x) {
        if (x + val == target || x - val == target || x == target)
            return true;
        return false;
    }

}
