Problem Statement

There is a stickpiece of chalk (corrected 11/8 7:20) of length $N$. Keisuke6 has decided to smash this chalk completely to pieces. To do so, he repeats the following operation until no chalk of positive length remains.

Randomly choose $1$ piece from among the chalks of length at least $1$ and drop it. Letting $n$ be the length of that chalk, it turns into 2 chalks of lengths $x$ , $n-x-1$. Here, $x$ is chosen with equal probability from among the integers between $0$ and $n-1$.

Input

$N$ 

$1 \leq N \leq 5000$
$N$ is an integer

Output

Print a newline at the end.

Sample

1

1.000000000