Consider the algorithm solve given below. This algorithm solves problem P by finding the output $($solution$)$ O corresponding to any input I.

void solve $($input I, output& O$)$

$\{$

if $($size$($I$)==1)$

find solution O directly;

else $\{$

partition I into $5$ inputs I$1,$ I$2,$ I$3,$ I$4,$ I$5,$ where sixe $($Ij$)=$ size$($I$)/3$ for j $=1,...,5$;

for$($j $=1$; j $<=5$; j$++)$

solve$($Ij$,$ Oj$)$;

Combine O$1,$ O$2,$ O$3,$ O$4,$ O$5,$ to get O for P with input I;

$\}$

$\}$

Assume g $($n$)$ basic operations for partitioning and combining and no basic operations for an instance of size $1.$

Write a recurrence equation T$($n$)$ for the number of basic operations needed to solve P when the input size is n$.$