Sagume finds that there is too much filth in Gensoukyou that she can't endure any more. She decides to clean up the Gensoukyou. There are N places in Gensoukyou which form a straight line, numbered from 1 to N. Places with the adjacent number can reach each other. To clean up all places, Sagume will follow the following procedure:

1. She randomly choose a place within the current connected component and clean it out. It will take her S seconds, in which S represents the current connected component's size.

2. She cut off the chosen place, then there will appear at most 2 new connected components.

3. She subsequently go to clean up the new components.

As a grand sage, Sagume is tight for time. She wants to know the expected time she will cost in order to schedule her time.

## 1209: Filth in Gensoukyou

时间限制: 1 Sec 内存限制: 128 MB Special Judge提交: 43 解决: 25

[提交][状态][讨论版]

## 题目描述

## 输入

The first line contains an integer T, the number of test cases.

Each test case contains an integer N, the number of places in Gensoukyou.

It is guaranteed that 1<=T<=1e4 and 1<=N<=1e6.

## 输出

For each test case, output one real number within a single line, which is the expected time(seconds) Sagume will cost. **Your answer will be considered correct if its absolute error does not exceed 1e-4.**

## 样例输入

```
2
3
4
```

## 样例输出

```
5.6667
8.8333
```

## 提示

## 来源

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All Copyright Reserved 2010-2020 Xidian Programming Contest Online Judge TEAM

GPL2.0 2003-2014 HUSTOJ Project TEAM

Anything about the Problems, Please Contact Admin:admin

All Copyright Reserved 2010-2020 Xidian Programming Contest Online Judge TEAM

GPL2.0 2003-2014 HUSTOJ Project TEAM