L. Grass Field
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Agronomist Bolzhedor has not visited his plot of land for ten years. Let's imagine that his plot of land has the shape of an infinite plane and during this time it has been overgrown with weeds. Bolzhedor wants to burn as much grass as possible, using as little effort and time as possible.

There are $$$n$$$ electric poles in the field. One way to get rid of the grass is to choose two poles and create an electric discharge between them. This will ignite the grass between the poles. After that, the fire will spread at a constant speed of $$$v$$$ meters per minute. Specifically, if we consider moments $$$T_0$$$ and $$$T_1=T_0+t$$$ (where $$$t$$$ is the time in minutes), point $$$X$$$ will be on fire at moment $$$T_1$$$ if and only if there is a point $$$Y$$$ that was on fire at moment $$$T_0$$$ and the length of segment $$$XY$$$ is not greater than $$$vt$$$.

There is one problem: according to the forecast, it will rain in $$$H$$$ hours and extinguish all the grass. Find the largest area of grass that Bolzhedor can burn using the electric poles.

Input

The first line contains three integers separated by spaces: $$$n$$$ — the number of poles, $$$H$$$ — the time until the rain starts in hours, and $$$v$$$ — the speed of fire spread in meters per minute ($$$2 \leqslant n \leqslant 100$$$; $$$1 \leqslant H \leqslant 12$$$; $$$1 \leqslant v \leqslant 100$$$).

Each of the following $$$n$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ — the coordinates of the $$$i$$$-th pole in meters ($$$-10000 \leqslant x_y,y_i \leqslant 10000$$$). It is guaranteed that the positions of all $$$n$$$ poles are distinct.

Output

Output a single real number — the largest area of grass that can be burned, in square meters.

Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$. Specifically, let your answer be $$$a$$$ and the jury's answer be $$$b$$$. Your answer will be accepted if $$$\frac{|a-b|}{\max(1,b)} \leqslant 10^{-6}$$$.

Example
Input
3 2 1
1 0
-1 1
0 0
Output
45775.59052629