$.$ Referring to Figure Q$4,$ what is the path used $($a$)$ from $1$a to $5$a $($b$)$ from $1$a to $6$a$,$ respectively,

using the following routing algorithms?

$1.$ The shortest path routing

$2.$ The hot potato routing $($with the shortest path routing outside AS$1)$

$3.$ BGP routing with the elimination rules:

i$.$ shortest AS$-$PATH

ii$.$ shortest path to NEXT$-$HOP