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 \(v\).

Problem credits: Lewin Gan

Problem credits: Lewin Gan

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 \(i-1\).

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