Anagram Density Sort

Given a list of words, sort them based on the 'density' of their anagram group. Specifically, sort by the total number of times any anagram of that word appears in the input list (descending). If densities are equal, sort by the alphabetically sorted version of the word (ascending). If still tied, sort by the original word (ascending). Example: Input: 'cat dog act tac god' - 'cat', 'act', 'tac' are anagrams. Group size: 3. - 'dog', 'god' are anagrams. Group size: 2. Output: act cat tac dog god