Shuffle n items uniformly at random. Return the probability that no item ends up where it started, which is called a derangement.

$$P = \sum_{j=0}^{n} \frac{(-1)^j}{j!}$$

The answer converges to $1/e \approx 0.3679$ almost immediately, and barely moves after n = 5 no matter how large n gets.

Input

5

Output

0.3666666666666667