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Share-based Payments - Share-based Compensation Expense (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2021
Feb. 29, 2020
Feb. 28, 2021
Feb. 29, 2020
Share-based Payment Arrangement [Abstract]        
Share-based payment expense $ 7.5 $ 8.0 $ 15.2 $ 24.7