Need help with CountIF when counting rows of 2 columns and comparing a 3rd columns value

I need to count the number of times a customer contact is made and if that customer is a top tier customer. So for example count column A or Column B if Column C = YES. Then also count Column A and column B is Column C = NO. I have attached an example spreadsheet with some mock data if anyone can help.

I think I need to use a COUNTIF vs a SUMPRODUCT, but I am not sure how to add in the 3rd check of Column C being a YES / NO?

Thank you everyone.Customer Contacts per Top Tier Clients - example.xls

Sorry i should have noted that there are two workbooks in this doc. The first is the data and the second is results. I manually filled in the correct results on the 2nd workbook. I just need those numbers to be automatically calculated.