We have an old staircase that runs into the basement (it is the original house basement staircase that would have originally allowed basement access from the outside but now is part of a new addition to the house) and I would like to frame it as a cedar closet. The stairs run over a bathroom and I would like to add a cedar closet under the stairs. What would be the best way to insulate such a space? On the outside of the cedar closet? Or rigid foam insulation on the stringers of the stairs? Thank you.