$[25$ points$]$ Fill out the following table for the given memory reference stream on a bus$-$

based shared$-$memory machine that supports the Dragon protocol. Show the state transition

of each processor and the bus transactions. All of the references are to the same memory

location X: r$/$w indicates read or write, and the digit refers to the processor issuing the

reference, e$.$g$.,r1$ means processor $P1$ reads X$.$ Assume that all caches are initially empty,

and all caches are write$-$allocated.

$r1,r3,w2,r2,r3,w1,w3,r1,r2,r3$