What is the order of growth of the solution to the Quicksort$-$like recurrence $F_N=\frac{1}{N}{\displaystyle \underset{1kN}{\overset{?}{}}}(F_{k-1}+F_{N-k})$ with $F_0=0?$

$0$

$1$

$\frac{1}{N}$

N

NlogN

$N^2$

$N^3$