Make Them Equal
Description
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.
Input
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 $a$.
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.
Samples
6
1 4 4 7 4 1
3
5
2 2 5 2 5
3
4
1 3 3 7
-1
2
2 8
3