UA-UMO 1999 Problem 105

Evaluate $$\lfloor\pi\rfloor+\left\lfloor\frac{\lfloor2\pi\rfloor}2\right\rfloor+\left\lfloor\frac{\lfloor3\pi\rfloor}3\right\rfloor+\ldots+\left\lfloor\frac{\lfloor1999\pi\rfloor}{1999}\right\rfloor.$$