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Endless Spin

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1070    Accepted Submission(s): 277


Problem Description
I spin it again and again,and throw it away finally.
So now I have a row of n ball,named from 1 to n,each ball is white initially.
At each step I randomly chose a interval [l, r] and paint all ball in this interval to black.
It means every interval have a equal chance of being chosen.
And I'll stop if all ball are black.What is the expected steps before I stop?
 

Input
The first line contains integer T(1<=T<=50). Denoting the number of the test cases.
Then T lines follows, each line contains an integer n (1<=n<=50).
 

Output
For each test cases,print the answer in a line.
Print the answer rounded to 15 decimal places.
 

Sample Input
3 1 2 3
 

Sample Output
1.000000000000000 2.000000000000000 2.900000000000000
 

Hint

不建议使用long double
 

Author
WJMZBMR
 

Source
 

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