Write the functions f$1,$ f$2,$ f$3,$ f$4,$ f$5,$ f$6$ defined below in ascending order of growth rate. That is$,$ if function h$($n$)$ immediately follows function f$($n$)$ in your list, then it should be the case that f$($n$)=$ O$($h$($n$)).$

f$1($n$)=$ ncube logsquare n

f$2($n$)=$ nsquare logcube n

f$3($n$)=$ npowern

f$4($n$)=$ nsquare lg$($ncube$)$

f$5($n$)=$ n$!$

f$6($n$)=3$powern