a$.$ Disk I$/$O has been bought and read$/$write requests have been queued up$.$ Requests for I$/$O arrived for the following cylinders in this order. $(6$ points$)$ Range of cylinder $0-199.$ Show the work to get full points.

$10,93,110,34,192,49,87,3,123,159,185$

The read$/$write head just finished reading a sector on cylinder $50.$ If the disk scheduling algorithm is C$-$Scan, and assuming no new requests enter the queue, what would be the $3$rd cylinder accessed after $50?$ What is the total no of cylinder visits? $($Don$$t count $50$ as the $1$st access. The next access after $50$ is the $1$st$.)$Show the math to calculate the total cylinder visits.

b$.$ Consider the following page reference string: $(6$ Points$)$

$7,2,3,1,2,5,3,4,6,7,7,1,0,5,4,6,2,3,0,1$

The demand paging size is $3.$ How many page faults will occur with the LRU replacement

algorithm? Show the full work