Plane Division

Chef is working with lines on a 2-D plane. He knows that every line on a plane can be clearly defined by three coefficients A, B and C: any point (x, y) lies on the line if and only if A * x + B * y + C = 0. Let's call a set of lines to be perfect if there does not exist a point that belongs to two or more distinct lines of the set. He has a set of lines on a plane and he wants to find out the