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.

4 1 2
-2 4
1 1
-3 -2
4 0

59 6

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 $\frac{59}{6}$.

3 3 4
11 -7
2 8
-4 18

0 1

The area of the convex hull may be $0$.

10 5 7
-3677189 -8603516
3324282 8371380
-4445534 -865546
-1235744 -6761030
2732080 -9194939
8510740 4384715
-7326815 2451526
-2079912 1054509
2072791 -8408897
-4437202 -5184973

6746232144385823 48

• Source: AtCoder ABC 478 G