# Ronaldo, Arnoldo and Ornaldo

Sometimes,two or more people may have names that are anagrams of each other. Let us call a group of distinct names that are all anagrams of each other an anagramic tuple.

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.

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