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Share-Based Compensation (Narrative) (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2021
May 31, 2020
May 31, 2021
May 31, 2020
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]        
Share-based compensation expense $ 1.0 $ 1.5 $ 5.3 $ 4.1