Enigmatic Travel

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Suhan and Laina live in an n-dimensional city where there are (n+1) locations.
Any two locations (consider these locations as points) are equidistant from
each other and connected by only one bi-directional road. They love to roam
together around the city on their favourite bi-verbal (A kind of vehicle). Kiri,
a tenth generation robot also lives in the same city and wants to kill Suhan
out of jealousy. That is why Suhan and Laina are very careful about keeping
their thoughts and plans secret. Therefore nobody knows a) Where Suhan and Laina
lives. b) What their destination location is. c) Which roads will they use?

So their journey can start from any location, ends in another location and they
may use any road sequence they like. Their destination location may be same
or different than the source location. For example when their tour is guaranteed
to be a simple cycle their source and destination location are same.

Given the number of locations in the city (L) you will have to find the expected
cost (often considered as average) of one of their single travelling. You can
assume that the cost of travelling from one location to another through the
direct (also shortest) path is 1 universal joule.

**Input**

The input file contains several lines of input. Each line contains a single
integer L(15 >= L > 2) that indicates the number of locations in the city.
Input is terminated by a line where value of L is zero. This line should not
be processed.

**Output**

For each line of input produce one line of output. This line contains three
floating-point numbers F1, F2, F3. Here F1 is the expected cost when they travel
along a path, F2 is the expected cost when it is guaranteed that they travel
along a simple path and F3 is the expected cost when it is guaranteed that they
travel along a simple cycle. All the floatingpoint numbers should be rounded
up to four digits after the decimal point. You must assume that their travelling
cost is not greater than (L). Travelling cost is always expressed in universal
joule.

**Sample Input**

3

4

5

0

**Sample Output**

2.4286 1.5000 3.0000

3.5500 2.2000 3.5000

4.6716 3.0625 4.2000

Source:

**Asia 2002, Dhaka (Bengal)**
Submit
Status