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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2022
May 31, 2021
May 31, 2022
May 31, 2021
Aug. 31, 2021
Income Tax Disclosure [Abstract]          
Effective Income Tax Rate Reconciliation, Percent 9.80% (6.80%) 6.70% (3.40%)  
Unrecognized Tax Benefits that Would Impact Effective Tax Rate $ 114.6   $ 114.6   $ 114.3