Consider a machine with four $(4)$ page frames and seven $(7)$ pages that is processing the following reference string, $w($Note that memory is initially empty.$)$: $w=0,1,5,4,3,4,5,3,6,3,2,0,2,0$

a$.$ Show the changes that occur in memory as the machine processes $w$ using the Least$-$ Recently Used paging algorithm. $($The tie$-$breaking rule is First$-$In$-$First$-$Out$)$ Show all workings.

b$.$ Show the changes that occur in memory as the machine processes $w$ using Belady's Algorithm. $($The tie$-$breaking rule is First$-$In$-$First$-$Out$)$ Show all workings.