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 N-sided 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 N-sided 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

Added by:Matthew Reeder
Date:2006-10-29
Time limit:1s
Source limit:30000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Al-Khawarizm 2006

hide comments
2015-05-27 01:43:29 DHEERAJ KUMAR
My 50th :D
2015-05-21 17:16:00 burninggoku
learned something new..
2015-02-22 08:29:27 Archita Goyal
Use double rather than float, caused me one WA!
2015-02-17 02:14:18 chicapi
Please correct the typo "die" -> "dice"?

[reply by cyclops: That is not a typo. Die is the singular of dice.]

Last edit: 2015-02-17 02:31:29
2014-12-24 21:03:22 Ashish Sareen
try this... www.codechef.com/problems/RRPLAYER
2014-07-28 09:17:06 Tizen
my 20th :D
2014-04-21 09:38:23 UJtriumphsâ„¢
thanx@ Prakhar Agarwal
2014-04-16 13:58:28 innovolt
mathematical stuff......
2013-09-01 16:36:59 RISHABH JAIN
nice question
2013-04-18 20:41:20 moustafa maher
All thanks to salem
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