$1.$ Edge$-$Triggered Clocking $(25$ points$)$

The system below contains two edge$-$triggered flip$-$flops connected by some combinational logic:

a$.$ Assuming zero clock skew, what is the minimum clock period?

b$.$ Given the clock period found in part $($a$),$ explain whether the system would work for each of the following scenarios. If not, how could we change the clock period to meet timing?

i$.$ The clock arrives $1$ ns late to flip$-$flop $2.$

ii$.$ The clock arrives $1$ ns early to flip$-$flop $2.$

iii. The clock arrives $3$ ns early to flip$-$flop $2.$

c$.$ Given the clock period found in part $($a$),$ how early can the clock arrive at flip$-$flop $2($relative to the clock edge at Flip$-$Flop $1)$ such that the circuit still works without any timing violations?

d$.$ Can you add any clock skew $($positive or negative$)$ to decrease the minimum clock period found in part $($a$)?$ If so$,$ what is the new period? If not, then why not?