Too Many Pawns on a Chessboard

In how many ways can I arrange 3232 black and 3232 white pawns on an 8×88 \times 8 chessboard such that no pawn attack another?

  • A black pawn can attack only a white pawn, and vice versa.
  • The usual chess rules of attacking follow, i.e, white pawns attack squares immediately diagonally in front, and the black pawns attack squares immediately diagonally backward (as seen by the white observer).
  • All rotation, reflections count as distinct.

For reference:

  • There are 33 such configurations on a 2×22 \times 2 board with 22 white and black pawns each.
  • There are 3030 such configurations on a 4×44 \times 4 board with 88 white and black pawns each.
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