the given MIPS$32$ benchmark program below computes factorial, Suppose you implemented PUSH $n and POP the former pushes $($Sn$)$ onto the stack and the latter pops off TOS into $n while SP is adjusted automatically. Rewrite this program PUSH and POP. b$)$ How many memory cycles do you save when calculating m$!?$

fact: addi$$1,$ $$0,1$ # initialize reg. $1$ to $1$

beq$$4,$ $$0,$ return$1$# if $($n $==0)$ then gotoreturn$1$:

bne$$4,$ $$1,$ continue # if $($n $!=1)$ then gotocontinue:

return$1$: addi$$2,$ $$1,0$ # assign result $=1$

jr$$31$ # return

continue: addi$$29,$ $$29,-12$ # allocate stack space for fp$,$ ra$,$ n

sw$$30,8($$$29)$ # save frame pointer

sw$$31,4($$$29)$ # save return address

addi$$30,$ $$29,8$ # update frame pointer

sw $$4,0($$$29)$# save n

addi$$4,$ $$4,-1$ # make n$-1$

jalfact # recursive call to fact$($n$-1)$

lw $$4,0($$$29)$ # restore n

mult $$2,$ $$4$ # fact $($n$-1)*$ n

mflo$$2$ # put product in result reg.

lw$$31,4($$$29)$ # restore return address

lw$$30,8($$$29)$ # restore frame pointer

addi $$29,$ $$29,12$ # restore stack pointer

jr$$31$ # return