JQuery :: Reassigning Alternate Classes To Thumbnails After Filter

I have a grid of thumbnail divs, 3 columns wide, which alternate having the class .first, .second, .third, repeating for each row. The divs also have a class according to the category to which they are assigned. There is a menu which allows you to filter the thumbnails by category. So, when you choose a category, it hides any div that doesn't have a class with that category. What I need to do is, when the grid is filtered, somehow clear all the .first, .second, .third classes, and reassign them based on the items that remain visible.