For each sequence of insertions below, start with an empty 2-3 tree. Using distinct letters of the alphabet, devise a sequence of 7 insertions that maximizes the number of nodes in a 2-3 tree. Draw the corresponding left-leaning red-black tree. Using distinct letters of the alphabet, devise a sequence of 8 insertions that minimizes the number of nodes in a 2-3 tree. Draw the corresponding left-leaning red-black tree. Extrapolate the relationship between the number of nodes in a 2-3 tree (for fixed n) and the level of balance in the corresponding left-leaning red-black tree