Problem D
Sanic
Sanic Hegehog likes to go fast. While Sanic can run, he especially enjoys curling himself up into a ball and rolling really fast downhill through loops. Sanic tries and fails to count the number of rotations he makes while spinning through a loop: spinning so fast makes him dizzy and confused. You, Sanic’s faithful sidekick, try to help with the counting but it’s futile – all you see is a blue blur of movement when Sanic rolls around a loop so fast. Perhaps you can write a program to calculate the number of rotations instead?
To simplify things, we measure the world in terms of Sanic radii. While spinning through a loop, Sanic can be accurately modeled as a circle of radius $1$. Furthermore, the inside of the loops Sanic spins through can be modeled as circles with radius $r$ (measured in Sanic radii). We also know that $r$ will always be at least $1.10$ as Sanic does not attempt to spin through smaller loops. Sanic spins clockwise and he follows the loop counter-clockwise, as illustrated in the diagram.
You need to compute $x$, the number of revolutions it takes for Sanic to make exactly one complete lap in the loop. Sanic does not slip - he always has perfect contact with the inside of the loop. The loops are rigid and do not move at all. Remember to go fast and compute the answer quickly!
Input
The input contains a single line with one decimal number $r$: the radius of the loop relative to the radius of Sanic. The number $r$ is given in decimal form with exactly two digits and satisfying $1.10 \le r \leq 1000.00$.
Output
Print $x$, as specified above, with a relative or absolute error of at most $10^{-6}$.
| Sample Input 1 | Sample Output 1 |
|---|---|
2.00 |
1.00 |
