"Fischer Random" chess is a variant where pawns start on the second rank (as they normally would) but pieces are semi-randomly arranged on the first rank, subject to the constraints that the King must start between the Rooks, and the Bishops must start on opposite-colored squares. Black's pieces will always "mirror" White's, as they do in a traditional game of chess. This variant is also known as "Chess ___." What number, equal to the number of possible starting positions in this game, fills in the blank?
960