$[20$pts$]$ Answer the question for the circuit shown below.

$($a$)(2$pts$)$ Find $V_{GS1}$ and $V_{GS2}$ when $v_{in}=0.$

$($b$)(2$pts$)$ Find the transconductance of $M_1$ and $M_2$ transistors, $g_{m1}$ and $g_{m2}.$

$($c$)(2$pts$)$ Find the output common$-$mode level, $V_{\text{C}\text{M}\text{O}}*$

$($d$)(3$pts$)$ Find the max. input common$-$mode level, $V_{CM{I}_{-\text{m}\text{a}\text{x}}}.$

$($e$)(3$pts$)$ Find the max. differential input, $v_{i{n}_{m}ax},$ for the full current switching.

$($f$)(3$pts$)$ Find the DC gain.

$($g$)(5$pts$)$ Draw the bode plot $($magnitude only, x$-$axis: rad$/$s$,$ y$-$axis: $[$dB$])$

Assumption: input signal source has ideal output characteristic and load capacitance, $C_L,$ is much bigger than parasitic capacitance

$V_{TN}=|V_{TP}|=1V,{}_n{C}_{ox}=100{10}^{-6}\frac{A}{V^2},{}_p{C}_{ox}=50{10}^{-6}\frac{A}{V^2}$