You have every point with positive integer coordinates not greater than $N$ over the $x$ and $y$ axis available and you want to draw as many straight lines as you can, with the condition that every line must pass through one of those points on each axis and there are no parallel lines. How many lines can you draw? How many ways can you draw these lines to achieve this maximum?
These two images correspond to sample case where $N = 4$:
A line with an integer $N$ ($1 \le N \le 10^9$).