A production line at V$.$ J$.$ Sugumaran's machine shop has three stations. The first station can process a unit in $7$ minutes. The second station has three identical machines, each of which can process a unit in $27$ minutes $($each unit only needs to be processed on one of the three machines$).$ The third station can process a unit in $5$ minutes.

$$ is the bottleneck station, with a bottleneck time of $q,$ minutes per unit $($enter your response as a whole number$).$