Consider the following algorithm:

int f$($n$)$

$/*$ n is a positive integer and n is a power of two $*/$

if $($n$<=1)$ return n

int x $=$ f$($n$/2)$

for int i$=1$ to n$/2$ do

x $=$ x $+($i $*$ i$)$

$/*$ loop ends here $*/$

int y $=$ x $+$ f$($n$/2)$

int z $=$ y $+$ f$($n$/2)$

return z

Let T$($n$)$ be the time f$($n$)$ takes. Write a recurrence formula for T$($n$)($you do not need to solve the recurrence$).$