For the load inverter below with the given parameters, if W$1/$L$1=2$ m$/1$ m and W$2/$L$2=1$ m$/1$ m$,$ Cgd$1=0\mathrm{.}5$ fF$,$

Cbd$1=10$ fF$,$ Cbd$2=10$ fF$,$ Cgs$2=2$ fF$,$ CL $=1$ pF$,$ and ID$1=$ ID$2=100$ A$,$ then:

$($Part $1)$ Calculate the output$-$voltage swing limits for VDD $=5$ V$.$

$($Part $2)$ Calculate the small$-$signal gain and the output resistance.