There are n horses on the platform of a merrygoround at amusement park. Horses are installed evenly along the circle. Merrygoround makes one full revolution in n seconds. When a kid wants to get on the merrygoround, 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 merrygoround use the described algorithm and no kid ever get off it.
Calculate the expected time a kid will have to wait at the merrygoround, depending on
the number of kids that are riding the merrygoround at the moment.
Input
The only input line contains an integer n (2 ≤ n ≤ 20).
Output
Output n lines. The ith line should contain the only number, which is the expected
number of seconds a kid will have to wait near the merrygoround if i − 1 kids are riding it. All
numbers should have absolute or relative error not exceeding 10^{−6}.
Sample
input  output 

4
 0.000000
0.250000
0.687500
1.500000

Problem Source: Tavrida NU Akai Contest. Petrozavodsk Summer Session, August 2010