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 $$$[4, 4, 4, 4]$$$. Input Format: 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 Format: 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. Note: None