a$.$ Construct a $2-3$ tree for the list A$,$ L$,$ G$,$ O$,$ R$,$ I, T$,$ H$,$ M$.($Use the alphabetical order of the letters

and insert them successively starting with the empty tree.$)$

b$.$ Assuming that the probabilities of searching for each of the keys $($i$.$e$.,$ the letters$)$ are the same,

find the largest number and the average number of key comparisons for successful searches in this

tree.