Illustrate what happens when the sequence 1, 5, 2, 4, 3 is added to an empty ScapegoatTree, and show where the credits described in the proof of Lemma 8.3 go, and how they are used during this sequence of additions.

I'm seen multiple versions of this and am still foggy even on how scapegoat trees work. If an answer to the question and additionally explanation on how scapegoat trees work, that would be great!

Lemma 8.3: Starting with an empty ScapegoatTree any sequence of m add(x) and remove(x) operations causes at most O(mlogm) time to be used by rebuild(u) operations.