Trading Places: Queenside

From the same position — the pearl of the collection: the "pirouette" castling. The king stands on d1, the rook on c1, and after queenside castling they will exchange squares exactly: the king takes c1, the rook takes d1. No other piece on the board is capable of such a thing. The doubting beginner looks for a trick here — there is no trick, only the strict logic of the final squares. King — onto the rook c1, if you would be so kind.