satisfying the Kraft inequality, one can construct a prefix code with codeword lengths equal to each formula_35 by choosing a word of length formula_35 arbitrarily, then ruling out all words of greater length that have it as a prefix. There again, we shall interpret this in terms of leaf nodes of an formula_2-ary tree of depth formula_13. First choose any node from the full tree at depth formula_39; it corresponds to the first word of our new code. Since we are building a prefix code, all the descendants of this node (i.e., all words that have this first word as a prefix) become unsuitable for inclusion in the code. We consider the descendants at depth formula_13 (i.e., the leaf nodes among the descendants); there are formula_41 such descendant nodes that are removed from consideration. The next iteration picks a (surviving) node at depth formula_42 and removes formula_43 further leaf nodes, and so on. After formula_33 iterations, we have removed a total of