$($b$)$ Consider the following page reference string:

$1,2,3,4,2,1,5,6,2,1,2,3,7,6,3,2,1,2,3,6$

If a system consists of four frames, how many page faults will occur for the following replacement algorithms?

$($i$)$ FIFO

$($ii$)$ LRU

$($iii$)$ Optimal