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Share-Based Compensation (Narrative) (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2023
Feb. 28, 2022
Feb. 28, 2023
Feb. 28, 2022
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]        
Share-based compensation expense $ 1.7 $ 1.3 $ 3.3 $ 2.5