COUNTIF Multiple Column Criteria

Dear Forum,

Please see excel attached.
I need a formula to count how many products with product ID my competitor has available and I don't.

If Column A (Product ID) is not blank, count
If Column B (Me) cell is blank, count
If Column C (Competitor) cell is not blank, count

In the example attached, the result I'm looking for is 3 (products I have with ID that my competitor offers and I don't)
Please note that on each column there will be blank and non blank cells.

Your assistance will be greatly appreciated!!!

It works perfectly. Thank you so much for your prompt response!