Problem L
Secret Santa
Christmas comes sooner every year. In fact, in one oftforgotten corner of the world, giftgiving has already started in the form of a Secret Santa syndicate.
Everybody in the small town of Haircombe is going to put their name into a hat. This hat will be given a hearty shuffle, and then afterwards everybody will take turns once more in taking a name back from the hat.
The name each person receives is the name of the fellow citizen to whom they will send a gift.
Of course, one concern with this strategy is that some unfortunate citizens could wind up giving gifts to themselves. What are the chances that this will happen to any of the citizens of Haircombe?
Input

One line containing the number $N$ ($1 \le N \le 10^{12}$), the number of citizens who will take part in Secret Santa.
Output

One line containing one real number; the probability that one or more people wind up giving gifts to themselves.
All output must be accurate to an absolute or relative error of at most $10^{6}$.
Sample Input 1  Sample Output 1 

2 
0.50000000 
Sample Input 2  Sample Output 2 

3 
0.66666667 
Sample Input 3  Sample Output 3 

6 
0.63194444 