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Problem 2278 YYS

Accept: 99    Submit: 259
Time Limit: 1000 mSec    Memory Limit : 262144 KB

Problem Description

Yinyangshi is a famous RPG game on mobile phones.

Kim enjoys collecting cards in this game. Suppose there are n kinds of cards. If you want to get a new card, you need to pay W coins to draw a card. Each time you can only draw one card, all the cards appear randomly with same probability 1/n. Kim can get 1 coin each day. Suppose Kim has 0 coin and no cards on day 0. Every W days, Kim can draw a card with W coins. In this problem ,we define W=(n-1)!.

Now Kim wants to know the expected days he can collect all the n kinds of cards.

Input

The first line an integer T(1 ≤ T ≤ 10). There are T test cases.

The next T lines, each line an integer n. (1≤n≤3000)

Output

For each n, output the expected days to collect all the n kinds of cards, rounded to one decimal place.

Sample Input

4 1 2 5 9

Sample Output

1.0 3.0 274.0 1026576.0

Source

第八届福建省大学生程序设计竞赛-重现赛(感谢承办方厦门理工学院)

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