Suppose you are given a flash memory consisting of $4$ KB pages, and there are $1024$ pages. How many bytes of memory would the OS need to keep track of free space in the worst case $($all of flash memory is free$)$ if

$1.$ bitmap was used?

$2.$ linked list was used? Assume $2$ bytes$/$pointer$.$

Under what conditions would a linked list be more memory$-$efficient than a bitmap?