144 Visa Free

I am from Singapore and thinking to go China with 144 hours visa free transit.

My route is Singapore -> Macus (3 nights) -> Beijing (5 nights) -> Back to Singapore.

Will this work?

I saw this online:
An eligible transit route would be:
Country or Region A → One of the participating areas in Mainland China → Country or Region C
A refers to one of the 53 eligible countries.
C should be a different country from A.
My C is different from my A since I will be doing a stopover at Macau before heading to Beijing but just want to be safe!

Please help, thanks!