[romwell]

At this point, you're yak shaving, where the sane thing to do is simply to count the number of times each letter occurs.

Better complexity-wise as well, both in terms of speed and storage: O(n) and O(1), respectively. [1]

The proposed algorithm uses O(n) storage (to store the immense product), and given that integer multiplication complexity is somewhere between O(n) and O(n^2), we end up[2] with at least O(n^2) runtime complexity!

[1] ...assuming the input data is less than 15 million terabytes in size; O(n log n), O(log n) respectively for arbitrary length input. Storing the number of input bytes takes O(log n) space, and integer increment can take O(size).

[2]https://en.wikipedia.org/wiki/Computational_complexity_of_ma...