Lots of Triangles
Farmer John is thinking of selling some of his land to earn a bit of extra income. His property contains n trees, 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 = n * (n - 1) * (n - 2) / 6 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 .. n − 3, please help FJ determine how many of his L potential lots have value v.
Input
The first line contains n (3 ≤ n ≤ 300). The following n lines contain the x and y coordinates of a single tree; these are both integers in the range 0 .. 10^6.
Output
Output n − 2 lines, where line i contains a count of the number of lots having value i − 1.