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Share-based Payments - Narrative (Details) - USD ($)
shares in Thousands, $ in Millions
12 Months Ended
Aug. 31, 2025
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2021
Aug. 31, 2022
Jan. 31, 2022
Dec. 31, 2021
Omnibus Stock Compensation Incentive and Directors’ Equity Plans              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Number of shares authorized for issuance (in shares)           3,600 2,700
Number of shares available for grant (in shares) 600 700 1,000        
Stock options outstanding (in shares) 800 900 1,000   1,100    
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Shares outstanding of restricted stock (in shares) 200 300 300   300    
Unrecognized compensation cost $ 34.9            
Unrecognized compensation cost period of recognition (years) 1 year 4 months 24 days            
Fair value of shares vested $ 26.2 $ 22.9 $ 19.9        
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units | Grants awarded beginning 2022              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based compensation vesting period (years) 3 years            
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units | Grants awarded prior to 2022              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based compensation vesting period (years) 4 years            
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Stock options              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Unrecognized compensation cost $ 0.0            
Stock options outstanding (in shares) 800            
Award expiration term       10 years      
Intrinsic value of options exercised $ 13.9 $ 6.6 $ 0.5        
Total intrinsic value of stock options outstanding 166.1            
Total intrinsic value of stock options exercisable 166.1            
Total intrinsic value of stock options expected to vest $ 0.0            
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Stock options | Market Options              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based compensation vesting period (years)       4 years      
Stock options outstanding (in shares)       300      
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Performance stock units              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Shares outstanding of restricted stock (in shares) 300 300 200   200    
Share-based compensation vesting period (years) 3 years 3 years 3 years        
Unrecognized compensation cost $ 13.6            
Unrecognized compensation cost period of recognition (years) 1 year 4 months 24 days            
Fair value of shares vested $ 14.9 $ 5.0 $ 11.5        
Performance stock units outstanding 300            
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted Stock Units (RSUs)              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Shares vested (in shares) 27            
Employee Stock Purchase Plan              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Number of shares authorized for issuance (in shares) 1,500            
Number of shares available for grant (in shares) 1,000            
Employee discount on purchases of common stock 5.00%