Using the rules and goals of a Sudoku puzzle, there are many thousands of possible arrangements of digits that would satisfy the conditions for a proper Sudoku solution.

Given a proper Sudoku solution, how many distinct (unique) arrangements of the digits in the grid could be presented by simply swapping the digits in individual cells?

For example, change all the 9s to 1s and 1s to 9s would produce a different arrangement in the grid, but would still be a legitimate correct solution.

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