Unpublish Categories with No Products?

-- HikaShop version -- : 2.3.3
-- Joomla version -- : 3.3.6

Is there a way to automatically un-publish any categories that don't have a product associated with it? If not, is there a query that would do it?

I understand that it's possible to not show that category, but I'm using a third party menu structure that creates a menu item for any published category.

[EDIT]
To clarify:
• hikashop_product_category - shows the product_id and the category_id together in one table
• hikashop_category - shows the full list of category_id rows

So the query would accomplish the following:
IF a category from hikashop_category DOES NOT have a product_id associated with it in hikashop_product_category then SET hikashop_category.category_published to 0

If this could be done in a Mass Action, all the better!
[/EDIT]

Thanks for your help!

Thanks, Nicolas!

As a follow-up, I think there is a way to combine that into one query, for anyone who runs across this thread in the future... Nicolas, please correct me if there's any reason this won't work.

UPDATE #__hikashop_category hc SET category_published = 0 WHERE (SELECT COUNT(product_id) FROM #__hikashop_product_category hpc WHERE hpc.category_id = hc.category_id) < 1

Thanks again for your help!