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Share-Based Compensation (Narrative) (Details) - USD ($)
$ / shares in Units, $ in Thousands
3 Months Ended
Nov. 30, 2023
Nov. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Share-based compensation expense $ 1,600  
Share withheld for payroll tax obligations $ 1,575 $ 2,471
Restricted Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Shares to be settled in cash 2,861 2,112
Weighted average grant-date stock price of awards to be settled in cash $ 120.59 $ 156.16
Performance Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Vesting period 3 years  
Performance Stock Units [Member] | Minimum [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Percentage of awards actually earned 0.00%  
Performance Stock Units [Member] | Maximum [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Percentage of awards actually earned 200.00%