\problemname{Coloring Contention}

\noindent
This problem looks challenging on first glance.  We want to force
Bob to make at least $k-1$ color changes if the path length is at
least $k$; this is the best we can do.  And indeed, we can do
exactly that, by coloring the edges by their distance from node 1.
Initially we set all edges to uncolored.
Edges adjacent to node 1 all get red.  Then, edges adjacent to those
edges that remain uncolored get blue.  And so on, alternating colors,
until all edges are colored.  Essentially, the color of an edge is
the parity of the distance from the source node.  Edges that
connect nodes at the same distance from the source node can get any
color.

It is not necessary to actually color the graph; all you need do is
calculate the distance between the two graph nodes and return that
value less 1.  Since the number of nodes is at least 2, you don't
even need to worry about the case of a path length of 0.
