How to produce the Mary Suest of Mary Sues - and make it work

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I am only on the tenth chapter of the first of two chaptered fics by one Ilex, featuring one Anastasia Twigg-Jones, and I already know that, failing colossal flaws somewhere, this is going to enter the roster of favourites. Anastasia Twigg-Jones, Professor of Defence against the Dark Arts, lover of Severus Snape, friend of the Marauders, Lily Evans and Frank and Alice Longbottom, friend and mentor of Harry Potter, has every feature of the most abandoned Mary Sue - and is an absolute screaming delight, childish, charming and hilarious. Recommended.
http://www.fictionalley.org/authors/ilex/LAFL.html
http://www.fictionalley.org/authors/ilex/HBIAB.html