Reference strings: $7,0,1,2,0,3,0,4,2,3,0,3,0,3,2,1,2,0,1,7,0,1$

Given set of reference string, identify number of page faults for the following page replacement algorithms with $3$ frames in the physical memory.

$1.$ First$-$In$-$First$-$Out Algorithm $($FIFO$)$

$2.$ Optimal Page Replacement Algorithms

$3.$ Least Recently Used Replacement Algorithm $($LRU$)$