A1021.Lots of Triangles--Platinum

Farmer John is thinking of selling some of his land to earn a bit of extra
income. His property contains $n$ trees ($3 \leq N \leq 300$), each described
by a point in the 2D plane, no three of which are collinear. FJ is thinking
about selling triangular lots of land defined by having trees at their
vertices; there are of course $L = \binom{N}{3}$ such lots he can consider,
based on all possible triples of trees on his property.
A triangular lot has value $v$ if it contains exactly $v$ trees in its
interior (the trees on the corners do not count, and note that there are no
trees on the boundaries since no three trees are collinear). For every $v = 0 \ldots N-3$, please help FJ determine how many of his $L$ potential lots have
value $v$.

The first line of input contains $N$.
The following $N$ lines contain the $x$ and $y$ coordinates of a single tree;
these are both integers in the range $0 \ldots 1,000,000$.

Output $N-2$ lines, where output line $i$ contains a count of the number of
lots having value $i-1$.