CF76F Tourist

Tourist walks along the $ X $ axis. He can choose either of two directions and any speed not exceeding $ V $ . He can also stand without moving anywhere. He knows from newspapers that at time $ t_{1} $ in the point with coordinate $ x_{1} $ an interesting event will occur, at time $ t_{2} $ in the point with coordinate $ x_{2} $ — another one, and so on up to ( $ x_{n},t_{n} $ ). Interesting events are short so we can assume they are immediate. Event $ i $ counts visited if at time $ t_{i} $ tourist was at point with coordinate $ x_{i} $ . Write program tourist that will find maximum number of events tourist if: - at the beginning (when time is equal to 0) tourist appears at point 0, - tourist can choose initial point for himself. Yes, you should answer on two similar but different questions.

The first line of input contains single integer number $ N $ ( $ 1

The only line of the output should contain two space-sepatated integers — maximum number of events tourist can visit in he starts moving from point 0 at time 0, and maximum number of events tourist can visit if he chooses the initial point for himself.