CF630Q.Pyramids

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.

IT 城市政府因埃及金字塔的盛名而不得安宁。该市计划在一处名为“翠谷”（Emerald Valley）的地点建造一座金字塔群。该建筑群的独特之处在于，其金字塔不仅有如埃及那样的四棱锥，还包括三棱锥和五棱锥。当然，城市预算中用于建造的资金数额取决于这些金字塔的体积。你的任务是计算一个试点项目（由三座金字塔组成——一座三棱锥、一座四棱锥和一座五棱锥）的总体积。

第一座金字塔的底面为等边三角形，且该金字塔全部 6 条棱长度均相等；
第二座金字塔的底面为正方形，且该金字塔全部 8 条棱长度均相等；
第三座金字塔的底面为正五边形，且该金字塔全部 10 条棱长度均相等。

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.

输入仅包含一行，其中为三个整数 $l_3$、$l_4$、$l_5$（$1 \leq l_3, l_4, l_5 \leq 1000$），分别表示三角锥、四角锥和五角锥的棱长。

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

输出一个数字——金字塔的总体积。绝对或相对误差不应大于 $10^{-9}$。