## USACO 2016 December Contest, Platinum

## Problem 1. Lots of Triangles

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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.

Contest has ended. No further submissions allowed.
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 $v$.

#### INPUT FORMAT (file triangles.in):

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 FORMAT (file triangles.out):

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

7 3 6 17 15 13 15 6 12 9 1 2 7 10 19

#### SAMPLE OUTPUT:

28 6 1 0 0

Problem credits: Lewin Gan