5 Big Booms

Parsa is tired of FIT1047. The FIT1047 textbook has $n$ pages. Parsa decides to determine the average BOOM Power produced when closing the book quickly and forcefully.

Parsa randomly opens the book to a page, with each page being equally likely to be selected. If the book is opened to a certain page, the BOOM Power is equal to the smaller number of pages on either side of the book (this count can range from $0$ to $n$). Given the number of sheets in Parsa's book, calculate the expected BOOM Power. In other words, the expected BOOM Power is given by: $$\frac{\sum_{i = 0}^{n} \min(i, n - i)}{n + 1}$$ where $\min(a, b)$ is the smaller value of $a$ and $b$.

Input

The only line of input contains $n$ which is the number of pages in Parsa's book.

Output

Print the expected BOOM Power of the book. Any answer with absolute error not exceeding $10^{-6}$ will be accepted.

Constraints

• $1 \le n \le 2 \times 10^9$

Example 1

3

0.500000

Example 2

21

5.000000