Coupon Collector's Beverage Bottles

In this problem, you are given an integer n representing the number of different ball star names. Each name appears with an equal probability on the label of a beverage bottle. Your task is to calculate the average number of beverage bottles one needs to purchase in order to collect all n distinct names.

This is a classic Coupon Collector's Problem. The expected number of bottles required is given by the formula:

\[ E = n \times \left(\sum_{i=1}^{n} \frac{1}{i}\right) \]

Print the result rounded to 4 decimal places.

inputFormat

The input consists of a single integer n (1 ≤ n ≤ 10⁵), which represents the number of different ball star names.

outputFormat

Output the expected number of beverage bottles required to collect all names, rounded to 4 decimal places.

sample

1

1.0000