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1817. Merry-go-round

Time limit: 1.0 second
Memory limit: 64 MB
There are n horses on the platform of a merry-go-round at amusement park. Horses are installed evenly along the circle. Merry-go-round makes one full revolution in n seconds. When a kid wants to get on the merry-go-round, he approaches a random horse and tries to get on it. If it is occupied, the kid will wait until the horse near him is free. All kids who want to get on the merry-go-round use the described algorithm and no kid ever get off it.
Calculate the expected time a kid will have to wait at the merry-go-round, depending on the number of kids that are riding the merry-go-round at the moment.

Input

The only input line contains an integer n (2 ≤ n ≤ 20).

Output

Output n lines. The i-th line should contain the only number, which is the expected number of seconds a kid will have to wait near the merry-go-round if i − 1 kids are riding it. All numbers should have absolute or relative error not exceeding 10−6.

Sample

inputoutput
```4
```
```0.000000
0.250000
0.687500
1.500000
```
Problem Source: Tavrida NU Akai Contest. Petrozavodsk Summer Session, August 2010
Tags: none