(a) Construct a 2−3 tree for the list h, y, d, r, o, m, a, g, n, e, t, i, c. Use the alphabetical order of the letters to compare them 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.