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 swapping entire rows or entire columns?

For example, swap all the digits between the top two rows, so that all of to the digits originally in the second row are moved up one cell into the top row and all the digits originally in the first row are move down one cell into the second row. That swap would produce a different arrangement in the grid, but would still be a legitimate correct solution.

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