Consider the following statements about the heap sort algorithm:
A. The MAX-HEAPIFY procedure, which runs in O(lg n) time, is the key to maintaining the max-heap property.
B. The BUILD-MAX-HEAP procedure, which runs in O(lg n) time, produces a max-heap from an unordered input array.
C. The MAX-HEAP-INSERT procedure, which runs in O(lg n) time, implements the insertion operation.
D. The HEAP-INCREASE-KEY procedure runs in O(n lg n) time to set the key of a new node to its correct value.
Choose the correct answer from the options given below:

1. AA, B only
2. BA, C only
3. CB, D only
4. DA, B, C, D

Pick an option to check yourself, or open the answer below.