Consider a simpler problem first, where we are also given a direction vector
and want to construct sum of vectors that goes as far as possible in that
specific direction.
Vectors that should be included in the sum are those that form an angle of at
most 90 degrees with direction vector, while those that form an angle above 90
should be omitted.
To generalize the solution of the problem, consider all possible directions
by performing an angular sweep.