P1943 Local Maxima

Given a permutation. If an element is larger than all the elements before it, it is called a "Local Maxima". Now, in a randomly generated permutation of length $n$, find the expected number of elements that are "Local Maxima".

A single line containing a positive integer $n$.

Output a single real number representing the answer, rounded to eight decimal places.

There are $2$ permutations of length $2$: $(1, 2)$ and $(2, 1)$. In the former, both numbers are "Local Maxima"; in the latter, only the first number $2$ is a "Local Maxima". Constraints - For $30\%$ of the testdata, $n \leq 10$. - For $80\%$ of the testdata, $n \leq 10^6$. - For $100\%$ of the testdata, $1 \leq n < 2^{31}$. Translated by ChatGPT 5