Pyramids

题意翻译

你有一个正三棱锥、一个正四棱锥和一个正五棱锥。不过它们都是特殊的，因为它们中任何一个的棱长全都相等(如下图所示)。\ \ 现在给出它们各自的棱长$l_{3}$，$l_{4}$，$l_{5}$，求它们的体积和，精确到小数点后9位。

题目描述

IT City administration has no rest because of the fame of the Pyramids in Egypt. There is a project of construction of pyramid complex near the city in the place called Emerald Walley. The distinction of the complex is that its pyramids will be not only quadrangular as in Egypt but also triangular and pentagonal. Of course the amount of the city budget funds for the construction depends on the pyramids' volume. Your task is to calculate the volume of the pilot project consisting of three pyramids — one triangular, one quadrangular and one pentagonal. The first pyramid has equilateral triangle as its base, and all 6 edges of the pyramid have equal length. The second pyramid has a square as its base and all 8 edges of the pyramid have equal length. The third pyramid has a regular pentagon as its base and all 10 edges of the pyramid have equal length. 

输入输出格式

输入格式

The only line of the input contains three integers $ l_{3},l_{4},l_{5} $ ( $ 1<=l_{3},l_{4},l_{5}<=1000 $ ) — the edge lengths of triangular, quadrangular and pentagonal pyramids correspondingly.

输出格式

Output one number — the total volume of the pyramids. Absolute or relative error should not be greater than $ 10^{-9} $ .

输入输出样例

输入样例 #1

2 5 3

输出样例 #1

38.546168065709