A higher-dimensional version of a quadtree is known as an octree, since, in three dimensions it divides each cube into 8 subcubes and recursively constructs an octree for each nonempty subcube as a child. Suppose we are given such a threedimensional structure, but we are only interested in two of the three dimensions, since we can only display two-dimensional images on a computer screen. Describe an efficient method for converting an octree into a quadtree defined on two of the dimensions used to construct the octree.