407905: GYM102939 C Robot Snowman

Dr. Doof is lonely during the winter months, and is sad that his daughter, Vanessa, has not visited him for the holidays. Although a poor replacement, he decides that he wants to build a robot snowman. The structure of a robot snowman consists of a lower body, torso, and head. Each of these components is a solid metal cube with side lengths in ratio $$$5:3:1$$$. To feel more loved, the good doctor wants to make the largest "snowman" possible to give himself company (while still maintaining the ratio of dimensions). You can help him design this glorious creation by simply knowing the total amount of scrap metal available in cubic meters (Doof uses the metric system, and so should you).

A single positive integer $$$S$$$ ($$$1 \leq S \leq 10^9$$$) representing the total amount of scrap metal in cubic meters that Dr. Doof has for personal use.

A single positive number representing the side length in meters of the "head" of the robot snowman that Dr. Doof desires. Any answer within $$$10^{-3}$$$ of the judge solution will be accepted.

153

1.0000000000

216

1.1218137878