Monotone grid paths hitting at least one power-up

On a $6\times6$ board a character starts at cell $(1,1)$ and must reach $(6,6)$, moving one cell at a time either down or to the right. Bonus items sit on cells $(2,3)$ and $(4,6)$. How many routes pass through at least one of the bonus cells?

$131$. Use inclusion-exclusion: routes through $(2,3)$ number $\binom31\binom73=105$, routes through $(4,6)$ number $\binom83\cdot1=56$, and routes through both number $3\cdot\binom52\cdot1=30$. So $105+56-30=131$.