230. Balanced Bracket Strings

Print how many different balanced strings can be made from n pairs of brackets.

n = 3 -> ((())) (()()) (())() ()(()) ()()() is 6... no, 5

Count them yourself for n = 3 before writing code. The answer is 5, and if you found 6 you counted one twice.

Build them by choosing one character at a time. You may open a bracket while you have any left, and you may close one only while more are open than closed. That second rule is what keeps every string valid.

Constraints - `0 ≤ n ≤ 19`