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: $$\displaystyle \frac{\sum_{i = 0}^{n} \min(i, n - i)}{n + 1}$$ 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

Input

3

Output

0.500000

Example 2

Input

21

Output

5.000000