How many of the first 1000 positive integers can be expressed in the form
\lfloor 2 x\rfloor+\lfloor 4 x\rfloor+\lfloor 6 x\rfloor+\lfloor 8 x\rfloor,
where x is a real number, and \lfloor z\rfloor denotes the greatest integer less than or equal to z ?