$1.$ Consider the following page reference string:

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

How many page faults would occur for the following replacement algorithms, assuming one, three, five, six, and seven frames? Remember that all frames are initially empty, so your first unique pages will cost one fault each

Number of Frames

$1$

$3$

$5$

$5$

$7$

LRU

FIFO

OPTIMAL