ID of Hut from altitude (2500 m)

This weather was amazing this weekend and I went skiing and finally up to the Schilthorn to ski all the way down

I took this shot on the way from Birg-Schilthorn, direction WSW

I picked out there’s a hut in the distance. I thought it was Rothornhutte, but I don’t remember it being that prominent and we were way too high for it. In this direction there’s also Gspaltenhornhutte but that’s usually hidden on rock face… so is this Blüemlisalphütte?

But damn the weather was finnnne