Consider a B+-tree of order two (d=2). Thus, the maximum number of pointers per node is 5 and the maximum number of entries is 4.

a. Show the results of entering one by one the keys: ( 21, 12, 13, 45, 23, 67, 89, 79, 95, 11, 10, 14, 17, 33, 46, 28) (in that order) to an initially empty B+-tree. Show the state of the tree after every 4 insertions.

b. What is the utilization of the tree? The utilization of the tree is defined as the total number of entries in all the nodes of the tree (both leaf and non-leaf nodes) over the maximum number of entries that the same nodes can store.

c. Can you give a different insertion order of the same values that can create a tree with different height? If yes, provide the order. If not, explain why.