Similarity

Substitution in the Latin alphabet is a one-to-one mapping of each letter to another unique letter. Two words of the same length are called similar if there is a substitution that transforms one word into the other. For example, the words $\text{dog}$ and $\text{cat}$, as well as $\text{nine}$ and $\text{pope}$, are similar. However, $\text{dog}$ and $\text{pup}$, or $\text{nine}$ and $\text{four}$, are not similar.

Clearly, if two words are similar to a third word, then they are also similar to each other. Thus, any set of words can be partitioned into a certain number of groups of mutually similar words. The number of such groups is called the similarity index. For example, the similarity index of the set $\text{man}$, $\text{num}$, $\text{kid}$, $\text{mom}$, $\text{dad}$ is $2$, because the words $\text{man}$ and $\text{kid}$ form one group, and $\text{num}$, $\text{mom}$, and $\text{dad}$ form the other.

Given $N$ words, each of length $L$, determine the similarity index of this set of words.