Suppose that the file is not ordered by the nonkey field Department$\_$code and we want to construct a secondary index on Department$\_$code, using option $3$ of Section $17\mathrm{.}1\mathrm{.}3,$ with an extra level of indirection that stores record pointers. Assume there are $1,000$ distinct values of Department$\_$code and that the EMPLOYEE records are evenly distributed among these values. Calculate $($i$)$ the index blocking factor bfri $($which is also the index fan$-$out fo$)$; $($ii$)$ the number of blocks needed by the level of indirection that stores record pointers; $($iii$)$ the number of first$-$level index entries and the number of first$-$level index blocks; $($iv$)$ the number of levels needed if we make it into a multilevel index; $($v$)$ the total number of blocks required by the multilevel index and the blocks used in the extra level of indirection; and $($vi$)$ the approximate number of block accesses needed to search for and retrieve all records in the file that have a specific Department$\_$code value, using the index.