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
2013-01-28 22:07:42 saket diwakar
all thanks to wiki...:)
2012-11-15 17:26:16 Anirban
using float gives WA,why??
2012-09-06 17:13:19 ppo
@sarih i have checked for the case you have given but it still giving WA
2012-03-18 06:58:00 alphaplus
good tutorial on expectation value given on codechef.com
2011-02-20 20:22:36 Alex Anderson
@hari
It is asking for the expected value - it is a defined concept which can be a decimal. Check wikipedia.
2011-01-29 06:44:12 N Hari Prasad
how can the "number of times he throws" be a decimal??
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