Bessie has taken up the detailed art of bovine embroidery. Cows embroider
a cloth mounted in a circular hoop of integer radius d (1 <= d <= 50,000).
They sew N (2 <= N <= 50,000) threads, each in
a straight
line from one point on the edge of the hoop to another point on the edge of the
hoop (no two embroidered points share a location on the hoop's edge).
Being
mathematically inclined, Bessie knows a formula of the form ax + by + c = 0 for
each straight line piece of thread. Conveniently, a, b, and c are integers
(1,000,000 <= a <= 1,000,000; 1,000,000 <= b <= 1,000,000;
1,000,000 <= c <= 1,000,000). Even more conveniently, no two threads
coincide exactly.
Perhaps less conveniently, Bessie knows that her set of formula
coefficients also includes a number of formulae for threads that do not appear
to pass inside the hoop's circle. She regrets this greatly.
The origin (0,0) is in the precise middle of the hoop, so all points on
the hoop's edge are distance d from the origin. At least one of the coefficients
a and b is nonzero for each thread's formula.
Bovine embroidery is more highly regarded when the number of thread
intersections is maximized. Help Bessie: count the number of pairs of threads
that intersect on the cloth (i.e., within distance d of the origin). Note that
if three threads happen to coincide at the same point, that would be three pairs
of intersections. Four threads at the same point > six pairs of
intersections, etc.
