How varied was the ancestry of Old Kingdom Egyptians across different regions and social strata?

Egypt was a geographically diverse country, stretching from the Mediterranean coast in the north to the first Nile cataract in the south — a distance of more than a thousand kilometers.

Upper Egypt (the south) and Lower Egypt (the north) had different ecological environments, different agricultural practices, different cultural traditions, and different histories before unification.

Did they also have different genetic profiles?

And did the elite and non-elite at any given site share the same ancestry proportions, or were there significant differences by social class?