A full binary tree, a full quad$-$tree, and a full oct$-$tree have the same number of leaf nodes. Note that in a full quad$-$tree each node has four children, and in an oct$-$tree each node has eight children. Discuss the number of levels that need to be traversed in each of these trees from the root to the leaves. Which one is taller? Justify your answer in its general form. $[$Note: you may also take as example the number of leaves N as: $212].$