Problem Statement

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 $1 \leq i \lt j \leq N$.

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.

Input

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

Output

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.