My understanding is the tree structure should be preserved - only sibling nodes can be swapped to sorted order.
For instance, node 'b' is a child of node 'c' in my original data, and should still be a node of 'c' in the result. It is not.

I think the result should be

c
  b
    a
j
  e
    d
  h
    g
      f
  i
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