FAVDICE  Favorite Dice
BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an Nsided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question:
What is the expected number of throws of his die while it has N sides so that each number is rolled at least once?
Input
The first line of the input contains an integer t, the number of test cases. t test cases follow.
Each test case consists of a single line containing a single integer N (1 <= N <= 1000)  the number of sides on BuggyD's die.
Output
For each test case, print one line containing the expected number of times BuggyD needs to throw his Nsided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.
Example
Input: 2 1 12 Output: 1.00 37.24
hide comments
DHEERAJ KUMAR:
20150527 01:43:29
My 50th :D 

burninggoku:
20150521 17:16:00
learned something new..


Archita Goyal:
20150222 08:29:27
Use double rather than float, caused me one WA! 

chicapi:
20150217 02:14:18
Please correct the typo "die" > "dice"?


Ashish Sareen:
20141224 21:03:22
try this... www.codechef.com/problems/RRPLAYER 

Tizen:
20140728 09:17:06
my 20th :D 

UJtriumphsâ„¢:
20140421 09:38:23
thanx@ Prakhar Agarwal 

innovolt:
20140416 13:58:28
mathematical stuff...... 

RISHABH JAIN:
20130901 16:36:59
nice question 

moustafa maher:
20130418 20:41:20
All thanks to salem 
Added by:  Matthew Reeder 
Date:  20061029 
Time limit:  1s 
Source limit:  30000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  AlKhawarizm 2006 