Question 59
(USS 6) On the circle with center $O$ and radius $1$ the point $A_0$ is fixed and points $A_1,A_2,\ldots,A_{999},A_{1000}$ are distributed in such a way that $\angle A_0OA_k=k$ (in radians). Cut the circle at points $A_0,A_1,\ldots,A_{1000}$. How many arcs with different lengths are obtained?