We learned an efficient algorithm to build a binary heap: buildHeap$().$ There are two key steps:

Randomly populate initial heap with structure property

Perform a percolate$-$down from each internal node

Which of the following statements is FALSE?

A: Percolation$-$down only applies to internal nodes, rather than leaf nodes

B: Percolation down is used to fix the heap structure property.

C: The sum of the heights of all the internal nodes is upper bounded by

D: The first step guarantees the leaves are valid heaps implicitly.