Question $1-$ Asymptotic Bounds $[20\%]$ Rank the following functions by order of growth in increasing order and partition your list into equivalence classes such that two functions f$($n$)$ and g$($n$)$ are in the same class if and only if f$($n$)=\backslash$Theta $($g$($n$)).$ You do not need to prove your answer. $[$In this question, we assume logn stands for log$2$ n$.]($a$)$ n$\backslash$pi $,($b$)\backslash$pi n$,($c$)$ nn$,($d$)$ logn$,($e$)\backslash$pi logn$,($f$)$ nlog$\backslash$pi $,($g$)$ n log $\backslash$pi $,($h$)$ n log n$,($i$)$ n log logn$,($j$)$ log n log n$,($k$)\backslash$pi log$(2$n$),($l$)$ nlog$(2\backslash$pi $),($m$)$ n i$=1($i $+1),($n$)1910$n$!+316$nn