Need help planning itinerary and travel from Chiang Rai to Phayao to Chiang Mai

Hi dear folks of Reddit community, :)

We need your help with some local insights and information, while we plan our North Thailand trip for November. We are landing in DMK and taking a domestic flight to Chiang Rai. Planning to stay a night or two in CR, then a night or two in Phayao and later heading to Chiang Mai.

Can you please help us understand the Bus availability between these places? I've travelled from CR to CM earlier on a bus, but considering we have to do Phayao in between, are there buses from CR to Phayao and Phayao to CM?

Please do share any other information that can be useful to plan our trip around these places. Your help would be really helpful.

Thanks in advance.