Classify the following functions as $($i$)$ logarithmic, $($ii$)$ polynomial, and $($iii$)$ exponential, then put them in increasing order of asymptotic growth.

n$100,2$n$,$ n$2$n$,$ nlgn$,$ n$!,$ en$,$ n$2,$ lg$2$ n$,2$n$2,$ nn$,$ lgn$,$ nlgn$,$ lglgn$,$ n