We have a string of brackets, and we would like to make sure each bracket is properly opened and closed. The string has any number of (, ), [, ], {, and }. A valid string follows the common-sense rules of opening and closing brackets, so in other words, the formal rules are:
There are an equal number of opening and closing brackets of each type. Each bracket is opened first, and later closed using the same type of bracket.
While a specific bracket is open, every other enclosed pair of brackets that is opened should be closed before the encompassing bracket closes.
For example, {[()[]]()}() is valid, but [(]) is not. Given a string, your function should determine if it is valid or not.
Your function should output valid, or invalid depending on the given string.