The unclosed doors

Problem

Albor Manor woke up in silence. During the night, someone wrote a ( in the logbook every time a door opened and a ) every time one closed, but a few entries slipped past them.

The log makes sense if every ) closes a ( that came before it and nothing is left open at the end. Write a function that takes the log (a string made only of ( and ), possibly empty) and returns, as an integer, the smallest number of characters you'd have to add for it to make sense.

With ())( you return 2: the second ) has nothing to close and needs a ( before it, and the last ( is left open and needs a ). A stray ) isn't fixed by a ( that comes later: )( also gives 2.

An empty log already makes sense: you return 0.

Examples

• One left open

  "(()" → 1

• All in order

  "()()" → 0

• Closes before opening

  ")(" → 2

• An empty log

  "" → 0

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def missing_marks(log):
    pass

function missingMarks(log) {
}