$8.$ In a system where a process is allocated $4$ page frames, suppose that the page table in the following table shows the last loaded time of the page in each page frame $($in clock ticks from referenced $\backslash (($R$)\backslash )$ and modified $\backslash (($M$)\backslash )$ bits for each page. If a page fault occurs for virtual page $4,$ write which page frame will be replaced for each of the following memory management policies. Note that all numbers in the PTE below are decimal, all numbers are numbered starting from $0,$ and the page reference string is $\backslash (4,0,0,0,2,4,2,1,0,3,2[4\backslash )$ points$]$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Virtual Page $\backslash$# & Page Frame $\backslash$# & Time loaded & Time referenced & $\backslash ($ R $\backslash )$ bit & $\backslash ($ M $\backslash )$ bit $\backslash \backslash$

$2$ & $0$ & $60$ & $164$ & $1$ & $1\backslash \backslash$

$\backslash$hline $1$ & $1$ & $30$ & $166$ & $1$ & $0\backslash \backslash$

$\backslash$hline $0$ & $2$ & $150$ & $162$ & $0$ & $1\backslash \backslash$

$\backslash$hline $3$ & $3$ & $20$ & $163$ & $1$ & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$(1)$ Optimal

$(2)$ FIFO

$(3)$ LRU

$(4)$ CLOCK