5 - Minimum Cost Direction

Okabe wants to visit all of the $N$ distinct points $(x_{i},y_{i})$, $1 \leq i \leq N$ in the $2D$ plane. To do this he has to pick two vectors (or directions) $A$ and $B$ such that $A$ and $B$ are perpendicular. He can move along $A$ and $-A$ for a cost of $1$ per unit distance and move along $B$ and $-B$ for no cost at all (He can move real units too in these directions). He cannot move in any