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Share-based Payments - Share-based Compensation Expense (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2021
May 31, 2020
May 31, 2021
May 31, 2020
Share-based Payment Arrangement [Abstract]        
Share-based payment expense $ 7.1 $ 7.8 $ 22.3 $ 32.5