Given the following function$/$method foo

function foo$($L$,$ i$,$ j$)\{$

$//$ If the left$-$most element $i$ is larger than the right$-$

$//$ most element j

if

swap$(L,i,j)$

$\}$

$//$ If there are at least $3$ elements in the array

if

$t=$ floor $(\frac{j-i+1}{3})$

foo$(L,i,$ j$-$t$)//$ Recurse on the first $\frac{2}{3}$ of $L$

foo$(L,i+t,j$ Recurse on the last $\frac{2}{3}$ of $L$

foo$(L,i,$ j$-$t$)//$ Recurse on the first $\frac{2}{3}$ of $L$

$\}$

return L

$\}$

Assume $L$ is a $0-$indexed array of size $N.$

Let the starting values of i and $j$ be $0$ and $N-1$ respectively.

What is the worst case time complexity of the algorithm foo?

a$)O(N^{(lo{g}_{\frac{3}{2}}3)})$

b$)O(N^{(lo{g}_{3}3)})$

c$)O(N^{(lo{g}_{2}3)})$

d$)$ None of the above