CF603D Ruminations on Ruminants

Kevin Sun is ruminating on the origin of cows while standing at the origin of the Cartesian plane. He notices $ n $ lines  on the plane, each representable by an equation of the form $ ax+by=c $ . He also observes that no two lines are parallel and that no three lines pass through the same point. For each triple $ (i,j,k) $ such that $ 1

The first line of the input contains a single integer $ n $ ( $ 3

Print a single integer, the number of triples $ (i,j,k) $ with $ i<j<k $ such that lines  form an original triangle.

Note that in the first sample, some of the lines pass through the origin. In the second sample, there is exactly one triple of lines: $ y=1,x+y=2,x-y=-2. $ The triangle they form has vertices $ (0,2),(1,1),(-1,1) $ . The circumcircle of this triangle has equation $ x^{2}+(y-1)^{2}=1 $ . This indeed passes through $ (0,0). $