shunfurh
编程介的小学生
2017-11-12 15:42

Endless Spin

10
  • it
  • lines
  • each

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

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