Where Are All These Flies Coming From?

My house is being invaded by flies. I've never had anything quite like this happen. I've killed dozens, Aidan has killed dozens and so has Brendan.

We might let in one or two going in and out of the house, but I certainly can't account for all these that way. There is nothing in the house that is nasty or maggoty. The only thing I can think of is that possibly there is a dead animal in the attic or garage, and the flies are coming in through some crack. Yet, I can't find anything, and there is no odour to give me a clue.

There is a pretty rapid replacement factor, too. We go around and kill every fly in the place, and, half an hour later, there are a dozen more.

And, yes, I did check the litter boxes!

I think I may get some of those old-fashioned sticky fly paper spiral things. Just to give the house a nice classy atmosphere, you know?