Little Pony and Alohomora Part I

Trixie is a female unicorn pony and traveling magician, having been rumored to be "the most magical unicorn in all of Equestria". One day, Trixie arrives in Ponyville.


There is n boxes on the stage. There is a random key in each box and each box has a key match it. As a unicorn, Trixie can use "Alohomora"(the unlocking spell) to open any box.

Trixie would like to open all the boxes, also Trixie would like to minimize the spells she used. Help Trixie to calculate the expected number of spells she need to used in order to open all the boxes necessary.

Input contains multiple test cases (less than 100).
For each test case, only one line contains one integer n (1<=n<=1000000000).

For each case, output the corresponding result, rounded to 4 digits after the decimal point.

1
2

1.0000
1.5000

The second sample: There are two different permutations when n equal to 2: (1, 2) and (2, 1). Trixie need to use 2 spells in (1, 2) and 1 spell in (2, 1).

BestCoder Round #7