For the following functions, please indicate which one has the fastest growth rate according to the Big$-$O notation.

A: $5*$log$($n$)$ B: log$($log$($n$))$ C: n$/2+10$

D: n$*$log$($n$)$ E: $5$n $+100$ F: n$3+2$n$2+6$n$+24$

G: n$!$ H: n$*($n$+1)/2$ I: n