A system has $3-$page frames available in physical memory. The following sequence of page references occurs:

Page Reference String: $\backslash (2,3,3,8,8,8,1,2,4\backslash )$

Guided Instructions:

$1.$ Start with an empty memory. For each page reference:

$1.$ Determine if it's a hit or miss $($a miss leads to a page fault$)$

$2.$ Use the Least Recently Used $($LRU$)$ rule to replace the page that hasn't been used for the longest time

$2.$ After processing each page reference:

$1.$ Write down the current state of the memory frames

$2.$ Note whether it's a hit or a miss.

$3.$ Indicate which page was replaced $($if applicable$).$

Consider the following example for additional help:

Page Reference String: $\backslash (3,2,1,4,2,5,1,2,3\backslash )$ Fill in the table below based on the steps described above and the example given:

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

$\backslash$hline Step & Page Ref & Memory Frames & Hit$/$Miss & Page Replaced $\backslash \backslash$

$\backslash$hline $1$ & $2$ & & & $\backslash \backslash$

$\backslash$hline $2$ & $3$ & & & $\backslash \backslash$

$\backslash$hline $3$ & $3$ & & & $\backslash \backslash$

$\backslash$hline $4$ & $8$ & & & $\backslash \backslash$

$\backslash$hline $5$ & $8$ & & & $\backslash \backslash$

$\backslash$hline $6$ & $8$ & & & $\backslash \backslash$

$\backslash$hline $7$ & $1$ & & & $\backslash \backslash$

$\backslash$hline $8$ & $2$ & & & $\backslash \backslash$

$\backslash$hline $9$ & $4$ & & & $\backslash \backslash$

$\backslash$hline

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

Also, how many page faults occurred?