Consider the following algorithm:

int f$($n$)$

$/*$ n is a positive integer $*/$

if $($n$<=4)$ return n

int diff $=$ f$($n$-2)$ f$($n$-3)$

int cnt $=0$

for i$=1$ to n$-1$ do $\{$ if $($i $<=$ diff$)$ cnt$++$ ;$\}$

return f$($n$-1)+$cnt$+1$

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