$($U & G$-$required$)[20$ points$]$

$($a$)[10$ points$]$ Show how OS$-$SELECT $($T$.$root, $16)$ operates on the red$-$black tree shown in the figure below.

$($b$)[10$ points$]$ Show how OS$-$RANK $(T,x)$ operates on the red$-$black tree shown in the figure below and the node $x$ with $x*key=20.$

give working also for both a and b