Taxi Making Sharp Turns

Taxis of Kharagpur are famous for making sharp turns. You are given the coordinates where a particular taxi was on a 2-D plane at **N** different moments: $(x_1, y_1)$, $(x_2, y_2)$, ..., $(x_N, y_N)$. In between these coordinates, the taxi moves on a straight line. A turn at the i-th (2 ≤ i ≤ **N**-1) coordinate is said to be a *sharp* turn if the angle by which it turns at Point B = $(x_i, y_i)$