4337. Effective Gradient

Little W likes rational number $\frac{P}{Q}$ very much. He has n points on the plane. You need to tell him the closest gradient to $\frac{P}{Q}$ of the lines passing through at least two points.

Suppose a line passes through two points $(x_0,y_0)$ and $(x_1,y_1)$. The gradient of it is exactly $g=\frac{y0-y1}{x0-x1}$. Closest gradient means $$\underset{g\in G}{\arg min}|g-\frac{P}{Q}|$$ as $G$ is the set of gradients of all availible lines.