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.
The only input line contains an integer n (2 ≤ n ≤ 20).
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.
Problem Source: Tavrida NU Akai Contest. Petrozavodsk Summer Session, August 2010