2024 Mock AMC 10 - Problem 13

How many permutations of the word $TOPSOJ$ do not contain the words $``TOPS"$ or $``OJ"$ in them? For example, $TOPSJO$ and $TOJPOS$ are invalid, while $TOSPJO$ is valid.

$\textbf{(A)}~216 \qquad \textbf{(B)}~ 234 \qquad \textbf{(C)}~236 \qquad \textbf{(D)}~ 594\qquad \textbf{(E)}~ 596$