A12477. Make Them Equal

You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ integers.

You can choose any non-negative integer $D$ (i.e. $D \ge 0$ ), 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. $a_1=a_2=\dots=a_n$ ).

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 $[4, 4, 4, 4]$ .

The first line of the input contains one integer $n$ ( $1 \le n \le 100$ ) — the number of elements in $a$ .

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 100$ ) — the sequence $a$ .

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.