sentences:  For each non-leaf node "n" in a preferred path "P", it has a non-preferred child "c", which is the root of a new auxiliary tree.We attach this other auxiliary tree's root ("c") to "n" in "P", thus linking the auxiliary trees together.We also augment the auxiliary tree by storing at each node the minimum and maximum depth (depth in the reference tree, that is) of nodes in the subtree under that node.