Unique count of number of weeks worked per month

Salutations Gurus

I need to total the number of shows per month that employees worked on during a 12-month period.
Attached is the excel file with the job table in question.

The screenshot below shows the following highlighted dimensions of that table:

• Red, for name of the show;
• Blue, for the number of weeks worked in a month by the person in Job 1 and person in Job 2;
• Yellow, is the result I am trying to total.

The result should only count the number of shows that people worked on. Blank cells should not be counted. Notice, month 12 had no working shows.
Using standard COUNTA() or COUNTIF() will count each populated row of a show twice due to the two jobs that duplicate the rows for each show. This said, I need to count those duplicate rows in any given month as once, if populated; and uniquely as being part of 1 working show; and I can't seem to find the formula to do this correctly.

Thank you

Al