Score : $100$ points

问题陈述

假设从地面上 $x$ 米高的地方看到的地平线距离为 $\sqrt{x(12800000+x)}$ 米，求从地面上 $H$ 米高的地方看到的地平线距离是多少米。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Assuming that the horizon seen from a place $x$ meters above the ground is $\sqrt{x(12800000+x)}$ meters away, find how many meters away the horizon seen from a place $H$ meters above the ground is.

Constraints

• $1 \leq H \leq 10^5$
• $H$ is an integer.

Input

Input is given from Standard Input in the following format:

$H$

Output

Print the answer.
Your answer will be considered correct when the absolute or relative error from the judge's answer is at most $10^{-6}$.

Sample Input 1

333

Sample Output 1

65287.907678222

We have $\sqrt{333(12800000+333)} = 65287.9076782\ldots$. Outputs such as 65287.91 would also be accepted.

Sample Input 2

634

Sample Output 2

90086.635834623

We have $\sqrt{634(12800000+634)} = 90086.6358346\ldots$.

update @ 2024/3/10 10:18:42