Assume that you have built a dense B+-tree index on SSN, and the B+-tree's leaf nodes contain record ids pointing to data records in data file. Assume 10-byte long. Assume also that you built the tree by using bulk loading so that the nodes at each level were filled up as much as possible. 4. a. b. How many levels does the resulting tree have? For each level of the tree, how many nodes are at that level? How many block I/Os are needed to search for and retrieve a record from the file given its SSN value using the index How many levels would the resulting tree has with all pages 60% full only? c. d. 5. Repeat the above exercise when the B+ tree index is built on NAME. 6. Repeat the exercise when the B+ tree index is built on SSN, and the B+-tree's leaf nodes directly contain data records (there is no separate data file)