Consider a triangle $ABC$. The midpoints of the sides $BC, CA$, and $AB$ are denoted by $D, E$, and $F$, respectively. Assume that the median $AD$ is perpendicular to the median $BE$ and that their lengths are given by $AD = 18$ and $BE = 13.5$. Compute the length of the third median $CF$. (K. Czakler, Vienna)