408455: GYM103119 L Random Permutation

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 $$$\frac{|x - y|}{\max(1, |y|)} \leq 10^{-9}$$$.

2

1.000000000000

3

1.333333333333

50

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