Triangles

$n$ points are given on a plane. We are interested in the number of right-angled triangles with vertices at these points and area contained in the range $\[A,B]$.

The first line contains three integers $n$, $A$, $B$ ($1\leq n\leq 2000$, $1\leq A\leq B\leq 10^{18}$). The following $n$ lines describe the individual points. The $i$-th of these lines contains two integers $x\_i,y\_i$ ($-10^9\leq x\_i,y\_i\leq 10^9$) which are the coordinates of the $i$-th point. All the given points are distinct.

The only line of the output should contain the number of triangles with vertices at the given points and area in the range $\[A,B]$.