BLLUCK - Coincidence

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Toriel is planning to create a game with prize. In this game, there are N players and N boxes each containing a piece of paper with a player's name written on it. Each player has a unique name and each box contains a different name. There are at most 1000 players playing.

Then, each player take 1 box at random such that every player got a different box. The more player got a box containing their name, the bigger the prize is. To prepare the prize, Toriel needs your help to calculate the expected number of player to get their own name.

Input.

First line is T, number of games (T<1000). Next T lines each contains N for each game.

Output

For each game, output the expected number of players to get the box containing their own name. Output exactly 6 digits after decimal points.

Example

Input:
1
1 Output: 1.000000

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pandey101299: 2019-02-28 17:21:34

easy one

darryl: 2017-06-28 08:02:24

wow

gomathi ganesan: 2017-03-06 13:11:55

can anybody give some more test cases?

Jacob Plachta: 2017-01-31 04:13:32

Bounds need to be stated:

0 <= N <= 1000

Francky: 2016-11-24 18:21:40

a) hum hum... ok.. hum hum. AC.
b) On every problem where output is float, one should use 'Ignore fp errors 1e-?' as judge.

Andy: 2016-11-24 17:49:44

Input:
2
1
1
Output:
1.000000
1.000000

abdou_93: 2016-11-24 15:48:42

more test cases


Added by:Andy
Date:2016-11-23
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU
Resource:BLPCS5