$2.(15$ points$)$ Construct a finite state machine diagram that describes the following sequential circuit. The sequential circuit has three state bits $\backslash ($ A$\_\{2\},$ A$\_\{1\}\backslash ),$ and $\backslash ($ A$\_\{0\}\backslash ).$ Together, $\backslash ($ A$\_\{2\}$ A$\_\{1\}$ A$\_\{0\}\backslash )$ represent a three$-$bit unsigned number. There is a two$-$bit input op and a $($single bit$)$ output invalid.

The input op indicates the operation:

$00$ : increment by $1$

$01$ : increment by $2$

$10$: decrement by $1$

The input combination $11$ is unused and does not need to be included in the solution.

If the input operation would cause the number to go outside the range of a three$-$bit unsigned numbers, the new state is $000$ and the invalid output is $1.$ Otherwise, invalid is $0.$