Edit Step Ladders

An edit step is a transformation from one word $x$ into another word $y$ such that $x$ and $y$ are both words in the dictionary, and $y$ can be obtained from $x$ by adding one letter, deleting one letter, or changing one letter. For example, transforming dig into dog, or dog into do, are both edit steps.

An edit step ladder is a lexicographically ordered sequence of words $w_1, w_2, \ldots, w_n$ such that the transformation from $w_i$ to $w_{i+1}$ is an edit step for every $i$ with $1 \le i \le n-1$.

Given a dictionary, compute the length of the longest edit step ladder.

The input is a dictionary: a set of lower-case words in lexicographic order, one per line. No word is longer than 16 letters, and the dictionary contains at most 25000 words.

Output a single integer: the number of words in the longest edit step ladder.