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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2025
Feb. 29, 2024
Feb. 28, 2025
Feb. 29, 2024
Income Tax Disclosure [Abstract]        
(Benefit) provision for income taxes (33.00%) 21.60% (4.50%) 23.00%
Decrease in effective tax rate 54.60%   27.50%  
Expiration of statute of limitations, release of uncertain tax position $ 11.9