F.A.Q
Hand In Hand
Online Acmers
Problem Archive
Realtime Judge Status
Authors Ranklist
 
     C/C++/Java Exams     
ACM Steps
Go to Job
Contest LiveCast
ICPC@China
Best Coder beta
VIP | STD Contests
    DIY | Web-DIY beta
Author ID 
Password 
 Register new ID

Little Pony and Alohomora Part I

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 629    Accepted Submission(s): 344


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

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

Sample Input
1 2
 

Sample Output
1.0000 1.5000
 

Hint
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).
 

Source
 

Statistic | Submit | Discuss | Note
Hangzhou Dianzi University Online Judge 3.0
Copyright © 2005-2024 HDU ACM Team. All Rights Reserved.
Designer & Developer : Wang Rongtao LinLe GaoJie GanLu
Total 0.000000(s) query 1, Server time : 2024-07-14 10:09:47, Gzip enabled