Six Degrees of Cowvin Bacon    bacon.txt

The cows have been making movies lately, so they are ready to play a
variant of the famous game "Six Degrees of Kevin Bacon".

The game works like this: each cow is considered to be zero degrees
of separation (degrees) away from herself. If two distinct cows have
been in a movie together, each is considered to be one 'degree' away
from the other.  If a two cows have never worked together but have
both worked with a third cow, they are considered to be two 'degrees'
away from each other (counted as: one degree to the cow they've worked
with and one more to the other cow).  This scales to the general case.

The N (2 <= N <= 300) cows are interested in figuring out which cow
has the smallest average degree of separation from all the other cows.
excluding herself of course. The cows have made M (1 <= M <= 10000)
movies and it is guaranteed that some relationship path exists between
every pair of cows.

PROBLEM NAME: bacon

INPUT FORMAT:

* Line 1: Two space-separated integers: N and M

* Lines 2..M+1: Each input line contains a set of two or more
        space-separated integers that describes the cows appearing in
        a single movie.  The first integer is the number of cows
        participating in the described movie, (e.g., Mi); the
        subsequent Mi integers tell which cows were.

SAMPLE INPUT:

4 2
3 1 2 3
2 3 4

OUTPUT FORMAT:

* Line 1: A single integer that is 100 times the shortest mean degree
        of separation of any of the cows.

SAMPLE OUTPUT:

100

OUTPUT DETAILS:

Cow 3 has worked with all the other cows and thus has degrees of
separation: 1, 1, and 1 -- a mean of 1.00 .