Consider the following string of page references: $7,0,1,2,0,3,0,4,2,3,0,3,2.$

Given an empty main memory with $3$ page frames, find out the total number of page faults for the OPTIMAL page replacement algorithm. Count page faults only after all frames have been initialized.

Note: Assume the page reference string continues with $1,2,0,1,7,0,1$

$5.$a

$6.b$

$3*c$

$7.d$