Virtual memory. Considering the following page reference string:

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

How many page faults would occur for the following replacement algorithms, assuming four frames? Please show your calculation procedure. Remember all frames are initially empty, so your first unique pages will all cost one fault each.

a$)$ FIFO replacement

b$)$ Optimal replacement

c$)$ LRU replacement