 ## Problem 1. Lots of Triangles

Contest has ended. 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 $v$.

#### 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

Contest has ended. No further submissions allowed.