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Bored in Box

By AlbinHossain · Limits 1s, 512 MB

After becoming a demon, Nejuko can’t go out in the sunlight. Most of the daytime she stays in a box. Though she never complained, this is extremely boring to her. After all, why a demon (or human) would like to live in such a tiny box alone! That's why her elder brother Tanjiro decides to give her a problem to solve to bring some excitement.

Tanjiro drew an equilateral triangle ABCABC with its circumcircle. Then he drew three half circles each based on exactly the sides of the triangle. Finally, he got a figure like below.

Now Tanjiro gives the length of the side ABAB of the triangle and asks Nejuko to find out the area of the dark shaded region.

After trying for some times, Nejuko was almost close to the solution, she derived that the area of the given triangle is equal to 34BC2\frac{\sqrt{3}}{4}BC^2 and circumradius of the given triangle is equal to BC3\frac{BC}{\sqrt{3}}.

After doing this much stuff Nejuko started feeling tired. She needs to sleep now to gain some energy. Before going to sleep she asked you to solve the same problem.

She also said one more thing, “You must use 3.141593.14159 for the value of pipi(π)(\pi)”.

Input

The input will contain only one integer ABAB, the length of the one side of the triangle.

1AB3×1041\leq AB \leq 3\times10^4

Output

You have to output the area of dark shaded region. Your answer is considered correct if its absolute or relative error doesn't exceed 10610^{-6}.

Samples

InputOutput
14
110.526807904208283
InputOutput
6
20.300842268119887

Notes

  • An equilateral triangle is a triangle in which all three sides of the triangle have the same length.

  • Circumcircle of a triangle is the minimum radius circle that passes through all the vertices of that triangle. Circumradius is the radius of Circumcircle.

  • Half circles are exactly based on the sides of the triangle means the diameters of those half circles are equal to the respective sides of the triangle.

    Discussion

    Statistics


    100% Solution Ratio

    MursaleenEarliest, 1w ago

    MursaleenFastest, 0.0s

    MursaleenLightest, 0 B

    bokaifShortest, 75B

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    If we subtract the area of the circumcircle from the summation of area of triangle and area of the h...