AT_abc478_g [ABC478G] Division Point Hull

There are $ N $ points $ P_1,P_2,\dots,P_N $ on the coordinate plane. The coordinates of point $ P_i $ are $ (X_i,Y_i) $ . You are given positive integers $ p,q $ . Let $ Q_{i,j} $ be the point that internally divides the segment $ P_iP_j $ in the ratio $ p:q $ . In particular, if $ P_i=P_j $ , then $ Q_{i,j}=P_i $ . Find the area of the convex hull of $ Q_{i,j} $ for all pairs of positive integers $ (i,j) $ satisfying $ 1 \leq i \lt j \leq N $ .

The input is given from Standard Input in the following format: > $ N $ $ p $ $ q $ $ X_1 $ $ Y_1 $ $ X_2 $ $ Y_2 $ $ \vdots $ $ X_N $ $ Y_N $

It can be proved that, under the constraints of this problem, the area of the convex hull to be found is rational. When the area is represented as an irreducible fraction $ \dfrac{x}{y}\ (x \geq 0, y \geq 1) $ , output $ x $ and $ y $ in this order, separated by a space, in one line.

### Sample Explanation 1 We have $ Q_{1,2}=\left(-1,3\right),Q_{1,3}=\left(-\frac{7}{3},2\right),Q_{1,4}=\left(0,\frac{8}{3}\right),Q_{2,3}=\left(-\frac{1}{3},0\right),Q_{2,4}=\left(2,\frac{2}{3}\right),Q_{3,4}=\left(-\frac{2}{3},-\frac{4}{3}\right) $ . Their convex hull is the pentagon formed by connecting $ Q_{1,2},Q_{1,3},Q_{3,4},Q_{2,4},Q_{1,4} $ in this order, and its area is $ \frac{59}{6} $ .  ### Sample Explanation 2 The area of the convex hull may be $ 0 $ . ### Constraints - $ 2 \leq N \leq 10^5 $ - $ 1 \leq p \lt q \leq 10 $ - $ |X_i|\leq 10^7 $ - $ |Y_i|\leq 10^7 $ - All input values are integers.