Regular hexagon and triangles

Time limit2sMemory limit512 MB

Summary

Choose three non-crossing diagonals of a regular hexagon to maximize the smallest of the four resulting triangles' areas, for side length L.

Level: Easy3 of 10
Topics: Geometry, Greedy, Brute force
Solved: No attempts yet

Problem

You have a regular hexagon whose side length is $L$ . Drawing three diagonals that do not cross each other splits the hexagon into 4 triangles.

Let $S$ be the area of the smallest of those 4 triangles. The value of $S$ depends on which diagonals you draw. Write a program that finds the largest possible value of $S$ .

Input

The first line contains the side length $L$ of the regular hexagon. ( $1 \le L \le 1{,}000{,}000$ , $L$ is an integer)

Output

Print the largest possible value of $S$ on the first line, rounded half up to exactly six digits after the decimal point. Always print all six digits, including a final 0. The answer is always irrational, so the rounded value is uniquely determined.

Examples3

Example 1
Input
```
5
```
Expected output
```
10.825318
```
Example 2
Input
```
10
```
Expected output
```
43.301270
```
Example 3
Input
```
100000
```
Expected output
```
4330127018.922193
```