Is there some way to find the very cheapest hostel in a whole country?

I just had the urge to look up the cheapest hostel in all of Japan.

I tried each of HostelWorld, HostelBookers, and Hostels.com but each one had a mandatory requirement that I specify a city before giving me results.

I suppose I could find a list of all cities etc in Japan and search each in one of those sites and keep track of which hostel was cheapest in each, then finally sort that resulting list to find the cheapest of all. But where would I find a "complete" list cities with hostels, let alone hostels not in cities?

Is there some other accommodation search engine that doesn't require the city? Or some completely different method I haven't thought of?

I know prices fluctuate by season and such, that there are work-for-accommodation, that definitions of what's a hostel vs a guesthouse etc can vary. That's all fine, I'm talking about whatever similar criterion works for sites such as the ones I mentioned for one dorm bed, comparing prices for whatever date I search for.