Aaron is struggling with trigonometric functions, so his teacher gave him extra homework. Given an integer, $n$, he must answer the following question:

What is the maximum value of $sin(x)+sin(y)+sin(z)$, where $x}$, $y$, and $z$ are positive integers and $x+y+z=n$?

Help Aaron by finding this maximal value and printing it correct to ${9}$ decimal places.

Input Format

A single positive integer denoting $n$.

Constraints

$3\leq n\leq3\times10^{6}$

Output Format

Print a single real number rounded to a scale of exactly ${9}$ decimal places (e.g., $0.123456789$) denoting the maximum possible value.

Sample Input 0
3

Sample Output 0
2.524412954

Explanation 0

The only possible variant is $x=1$, $y=1$, and $z=1$, which gives us $sin(1)+sin(1)+sin(1)=2.524412954$

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