$(20$ points$)$ Assume $n$ is a power of $$6$$$.$ Assume we are given an algorithm $f$($n$)$$ as follows:

$\backslash$begin$\{$Verbatim$\}$

function f$($n$)$:

if n$>1$:

for i in range$(34)$:

f$($n$/6)$

for i in range$($n$*$n$)$:

print$("$Banana$")$

f$($n$/6)$

else:

print$("$Monkey$")$

$\backslash$end$\{$Verbatim$\}$

$\backslash$begin$\{$enumerate$\}[$label$=(\backslash$alph$*.)]$

$\backslash$item What is the running time for this function $f$($n$)$$$?$ Justify your answer. $($Hint: Recurrences$)$

$\backslash$begin$\{$solution$\}$

$[$Write your answer here$]\backslash$vspace$\{12$pt$\}\%$ delete this line and replace with your answer$/$work

$\backslash$end$\{$solution$\}$

$\backslash$item How many times will this function print $``$Monkey$"?$ Please provide the exact number in terms of the input $n$$.$ Justify your answer.