Question from Advent of Code 2015

Santa is trying to deliver presents in a large apartment building, but he can't find the right floor - the directions he got are a little confusing. He starts on the ground floor (floor 0) and then follows the instructions one character at a time.

An opening parenthesis, (, means he should go up one floor, and a closing parenthesis, ), means he should go down one floor.

The apartment building is very tall, and the basement is very deep; he will never find the top or bottom floors.

For example:

(()) and ()() both result in floor 0. ((( and (()(()( both result in floor 3. ))((((( also results in floor 3. ()) and ))( both result in floor -1 (the first basement level). ))) and )())()) both result in floor -3. To what floor do the instructions take Santa?