An integer sequence with length $n$, denoted by $a_1,a_2,\cdots,a_n$, is generated randomly, and the probability of being $1,2,\cdots,n$ are all $\frac{1}{n}$ for each $a_i$ $(i=1,2,\cdots,n)$.
Your task is to calculate the expected number of permutations $p_1,p_2,\cdots,p_n$ from $1$ to $n$ such that $p_i \le a_i$ holds for each $i=1,2,\cdots,n$.

The only line contains an integer $n$ $(1 \leq n \leq 50)$.

Output the expected number of permutations satisfying the condition. Your answer is acceptable if its absolute or relative error does not exceed $10^{-9}$.
Formally speaking, suppose that your output is $x$ and the jury's answer is $y$. Your output is accepted if and only if $\frac{|x - y|}{\max(1, |y|)} \leq 10^{-9}$.