Expected Number of Local Maxima in a Permutation

Given a permutation of n distinct numbers, we define a local maximum as an element that is larger than all the numbers preceding it. Since the first element has no preceding numbers, it is trivially a local maximum.

In a randomly generated permutation of length n, the expected number of local maxima is given by:

\( E = \sum_{i=1}^{n} \frac{1}{i} \)

Your task is to compute this expected value and output it with six decimal places of precision.

inputFormat

The input consists of a single integer n (1 ≤ n ≤ 10⁶), representing the length of the permutation.

outputFormat

Output the expected number of local maxima in the permutation, formatted to six decimal places.

sample

1

1.000000