3. Suppose eight current varieties of chipmunk (names 1-8) evolved from a common ancestral strain through an evolutionary process in which at various stages one ancestral variety split into two varieties (none of the ancestral varieties survive when they split into two new varieties). The resulting tree is binary (root has out-degree 1, in-degree 0; leaves have out-degree 0, in-degree 1; and remaining nodes have in-degree 1 and out-degreee 2). (a) Give an example of a tree that minimizes the maximum distance from each leaf to the root. (If this is confusing, try some trees of different shapes, and write the maximum distance from a leaf to the root-figure out which tree minimizes these distances). (b) What is the maximum possible distance from a leaf to the root? Give an example of a tree that achieves this maximum.