An i$-$node file system is defined as follows:

$$ There are $32$ direct pointers.

$$ There are $8$ single indirect pointers.

$$ There are $2$ double indirect pointers.

$$ There is one triple indirect pointer.

$$ The size of each block is $4$KB$.$

$$ The size of each pointer is $8$ bytes.

A$.$ What is the maximal size of a file in this system? Explain.

B$.$ What is the space overhead of the i$-$node structure for a $279$MB file in the

system? Explain.

C$.$ A program that reads a $4$MB file consecutively $($block by block from beginning to

end$)$ is executed. The system does not have a block$-$cache. How many disk

accesses will the program perform? Explain.

D$.$ An $18$ block block$-$cache is now added to the system. The block replacement

policy in the cache is LRU. How will your answer to part C change? Explain.