David Singmaster, in his book Notes on Rubik's "Magic Cube" (see the references in the Individual Research Projects), describes a sequence of moves to put the upper corners in place (after certain other moves). Using our notation, this set of moves is

\[F U^{2} F^{-1} U^{2} R^{-1} U R\]

Start with the standard-position cube and show the result after carrying out this sequence of moves.