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I'd frame up a dirt floor shed and cover the back and a portion of the sides with siding of your choice and cover the rest with welded wire, the opening size depends on the predators at your location. I'd put large over hangs all the way around to shed rain away from the coop and run and make it easier to have a nice vent on the back wall. I'd cover the insides up about 1' for deep litter.
JT