Aaron is struggling with trigonometric functions, so his teacher gave him extra homework. Given an integer, , he must answer the following question:
What is the maximum value of , where , , and are positive integers and ?
Help Aaron by finding this maximal value and printing it correct to decimal places.
Input Format
A single positive integer denoting .
Constraints
Output Format
Print a single real number rounded to a scale of exactly decimal places (e.g., ) denoting the maximum possible value.
Sample Input 0
3
Sample Output 0
2.524412954
Explanation 0
The only possible variant is , , and , which gives us