AT_abc478_g.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 $1 \leq i \lt j \leq N$.

平面上有 $N$ 个点 $P_1,P_2,\dots,P_N$。点 $P_i$ 的坐标为 $(X_i,Y_i)$。

给定正整数 $p,q$。记 $Q_{i,j}$ 为线段 $P_iP_j$ 上按比例 $p:q$ 内分所得的点。特别地，若 $P_i=P_j$，则定义 $Q_{i,j}=P_i$。

求所有满足 $1 \leq i \lt j \leq N$ 的正整数对 $(i,j)$ 所对应的点 $Q_{i,j}$ 构成的凸包的面积。

The input is given from Standard Input in the following format:

$N$ $p$ $q$
$X_1$ $Y_1$
$X_2$ $Y_2$
$\vdots$
$X_N$ $Y_N$

输入从标准输入中按以下格式给出：

$N$ $p$ $q$
$X_1$ $Y_1$
$X_2$ $Y_2$
$\vdots$
$X_N$ $Y_N$

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.

可以证明，在本题的约束条件下，所求凸包的面积为有理数。当该面积表示为既约分数 $\dfrac{x}{y}\ (x \geq 0, y \geq 1)$ 时，请在一行中按顺序输出 $x$ 和 $y$，中间用一个空格分隔。

Sample 1 Explanation:
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 2 Explanation:
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.

样例 1 解释：
我们有 $Q_{1,2}=\left(-1,3\right),Q_{1,3}=\left(-\frac{7}{3},2\right),Q_{1,4}=\left(0,\frac{8}{3}\right),Q_{2,3}=\left(-\frac{1}{3},0\right),Q_{2,4}=\left(2,\frac{2}{3}\right),Q_{3,4}=\left(-\frac{2}{3},-\frac{4}{3}\right)$。

它们的凸包是由按此顺序连接点 $Q_{1,2},Q_{1,3},Q_{3,4},Q_{2,4},Q_{1,4}$ 所构成的五边形，其面积为 $\frac{59}{6}$。

样例 2 解释：
凸包的面积可能为 $0$。

限制条件

• $2 \leq N \leq 10^5$
• $1 \leq p \lt q \leq 10$
• $|X_i|\leq 10^7$
• $|Y_i|\leq 10^7$
• 所有输入值均为整数。