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!!!