Count unique entries across columns based on criteria

I have a table of different trainer names (columns) and training sessions (rows)
I have formulas to count how many trainers took part in each training session and how many sessions each trainer has been doing.
Each training session has from 2 to 6 trainers.

I would now like to count the number of co-trainers each trainer has worked with.
In the attached example I have counted the Co-trainers manually in row 24. Does anybody know of a formula that can do the counting automatically.
I prefer not to use VBA.

Thanks
Peter