A patient experiences a stroke resulting in a sudden onset of ataxia (loss of co-ordination of voluntary muscle movements) and dysmetria (an inability to judge distance, leading to overshooting or undershooting targets during movement). However, their cognitive abilities, homeostatic thermoregulation, and breathing rhythm remain entirely unaffected.

The diagram below shows a sagittal section of the human brain with four regions labelled $P$, $Q$, $R$, and $S$.

Which labelled region has most likely been damaged by the stroke?