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Dear Math Freaks: Total unique chess notations

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chryoyo0

Format should be irrelevant, but let's use standard algebraic notation. Here is an example of me calculating notations of characters length seven.

Piece type, File, Rank, Capture, File, Rank, Check/Mate

5 * 8 * 8 * 1 * 8 * 8 * 2 = 40960

Now, how might we approach this problem with all notation?

Oh and don't forget to add castling.