B. Make Them Equaltime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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].InputThe 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.OutputPrint 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.ExamplesInput
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

6
1 4 4 7 4 1

3 
['math', '*1200']