How many different values can $\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor$ take for $0 \leq x \leq 1$?

How many different values can \(\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor\) take for \(0 \leq x \leq 1?\)