A Rook in the King's Path

A most curious case, your attention please. The king on b1 is heading for kingside castling on g1, but directly in his path, on c1, stands… his own castling rook. The beginner will decide the path is blocked — and will be mistaken. The rule states: the path must be free of all pieces except the castling participants themselves. The king and rook will part ways elegantly in a single motion: he to g1, she to f1. If you please: king — onto the rook c1.