$(10$ pts$.)$ Find an exact closed$-$form formula for $M(n),$ the worst$-$case number of

$*\text{'}$s performed by the following algorithm on input $n,$ which is a power of $2$ :

int int $n$

$\{$

if $(n1)$

return $1$ ;

int ans $=1$;

for $($int $i=0$; $in$; $++$i$)$

ans $=$ ans $**i$;

return ans $*p2(\frac{n}{2})*p2(\frac{n}{2})$;

$\}$