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Share-based Payments - Narrative (Details) - USD ($)
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Aug. 31, 2018
Jan. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based payment expense $ 32,500,000 $ 38,200,000 $ 29,200,000    
Stock Incentive Plan          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Number of shares authorized for issuance (in shares)         2,700,000
Number of shares available for grant (in shares) 300,000 700,000 1,400,000    
Age to be attained allowing for continued vesting   60 years      
Years of service eligible for continued vesting 5 years 10 years      
Share-based payment expense $ 32,500,000 $ 38,200,000 $ 29,200,000    
Stock Incentive Plan | Restricted stock awards and units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares outstanding of restricted stock (in shares) 400,000 400,000 400,000 400,000  
Share-based compensation vesting period (years) 4 years        
Unrecognized compensation cost $ 28,100,000        
Unrecognized compensation cost period of recognition (years) 1 year 9 months 18 days        
Fair value of shares vested $ 19,500,000 $ 22,800,000 $ 26,900,000    
Granted (in shares) 200,000 200,000 200,000    
Share-based payment expense $ 15,100,000 $ 24,600,000 $ 25,100,000    
Stock Incentive Plan | Stock options          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Unrecognized compensation cost $ 17,000,000        
Unrecognized compensation cost period of recognition (years) 2 years 2 months 12 days        
Stock options outstanding (in shares) 1,200,000 900,000 400,000 300,000  
Award expiration term 10 years        
Intrinsic value of options exercised $ 1,200,000   $ 0    
Total intrinsic value of stock options outstanding 70,900,000        
Total intrinsic value of stock options expected to vest 42,800,000        
Total intrinsic value of stock options exercisable 27,400,000        
Share-based payment expense $ 9,200,000 $ 4,900,000 $ 2,700,000    
Stock Incentive Plan | Stock options | Service Options          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based compensation vesting period (years) 3 years        
Stock options outstanding (in shares) 800,000        
Granted (in shares) 0        
Stock Incentive Plan | 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) 400,000        
Granted (in shares)     0    
Stock Incentive Plan | Performance stock units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based payment expense $ 6,800,000 7,300,000 $ 0    
Supplemental Deferred Savings Plan | Performance stock units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares outstanding of restricted stock (in shares) 100,000        
Share-based compensation vesting period (years) 3 years        
Unrecognized compensation cost $ 3,800,000        
Unrecognized compensation cost period of recognition (years) 1 year 6 months        
Supplemental Deferred Savings Plan | Employee Deferred Stock Units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares vested (in shares) 7,000        
Share-based payment expense $ 0 $ 0 $ 0    
Directors' Deferred Compensation Plan | Restricted Stock Units (RSUs)          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Number of shares available for grant (in shares) 300,000 300,000 400,000    
Shares vested (in shares) 100,000        
Employee Stock Purchase Plan          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Number of shares authorized for issuance (in shares) 1,500,000        
Number of shares available for grant (in shares) 1,000,000        
Employee discount on purchases of common stock 5.00%