Ronaldo, Arnoldo and Ornaldo
For example (Norma, Ramon, Roman) is an example of an anagramic tuple of size \(3\).
In names.txt, a 46K text file containing over five-thousand first names, let the size of the largest anagramic tuple be \(N\). Let \(M\) be the number of anagramic tuples of size \(N\). What is the value of the product \(N \times M\)?
Details and assumption
The arrangement of the names in the tuple doesn't matter. I.e. (Tia, Tai) is the same tuple as the tuple (Tai, Tia).
All the names in an anagramic tuple are distinct.