Number of Valid Move Combinations On Chessboard

Count the number of ways to choose a destination square for each of n chess pieces (rooks, bishops, queens) on an 8×8 board so that, when all pieces simultaneously move one square per second along their allowed straight-line directions toward their destinations, no two pieces ever occupy the same square at the same time (direct one-second swaps are allowed). The core challenge is enumerating destination choices while enforcing pairwise spatiotemporal collision constraints along piece paths.