Colour the points by quadrant

The signs of the two coordinates choose the quadrant. You will sort a cloud of points, count each quadrant, and colour the points by where they fall.

The idea. Quadrant I is $(+, +)$, II is $(-, +)$, III is $(-, -)$ and IV is $(+, -)$. A point with a $0$ coordinate is on an axis: give it the number $0$.

Your tasks.

1. In quadrant, return $1$, $2$, $3$ or $4$, or $0$ for a point on an axis.
2. Fill counts so that counts[q] is the number of points with quadrant equal to q, for q from $0$ to $4$.
3. Fill colours with one colour per point, taken from palette by its quadrant number.