L. Random Permutation
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

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 $$$i=1,2,\cdots,n$$$.

Input

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

Output

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

Examples
Input
2
Output
1.000000000000
Input
3
Output
1.333333333333
Input
50
Output
104147662762941310907813025277584020848013430.758061352192