Background

(This problem has no hidden song... no need to guess.)

The final chapter of "The Story of Love and Sorrow, Part 1 · heartache."

After eating pizza, Yue Luo Wu Ti knew he had gone over his budget. To avoid embarrassing himself in front of Ai Yu Chou, he braced himself to settle the bill.

Problem Description

After paying, Yue Luo Wu Ti thought, "You ripped me off!" So when Ai Yu Chou asked how much it cost, Yue Luo Wu Ti replied with a bunch of gibberish. Ai Yu Chou said, "Forget it, I only ask: what is the price of the $n$-th dish?" Yue Luo Wu Ti wrote:

$$F_n=\dfrac{\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n}{\sqrt{5}}$$

Since Ai Yu Chou had studied programming, he computed $F_n$ in $1$ minute. Yue Luo Wu Ti was shocked. Can you, like Ai Yu Chou, compute the value of $F_n$?

Input Format

One line containing a non-negative integer $n$.

Output Format

One line containing a real number $F_n$, with two decimal places.

6

8.00

Hint

For all testdata: $0 \leq n \leq 48$.

Translated by ChatGPT 5