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Share-based Payments - Narrative (Details) - USD ($)
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Jan. 31, 2022
Dec. 31, 2021
Aug. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Share-based payment expense $ 37,400,000 $ 32,500,000 $ 38,200,000      
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)       3,600,000 2,700,000  
Number of shares available for grant (in shares) 1,100,000 300,000 700,000      
Share-based payment expense $ 37,400,000 $ 32,500,000 $ 38,200,000      
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Granted from October 2019 to September 2020            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Age to be attained allowing for continued vesting 60 years          
Minimum years of service for continued vesting of stock award 10 years          
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Fiscal 2021 grants            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Recipient years of service qualifying for non-forfeiture of awards 5 years          
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) 300,000 400,000 400,000     400,000
Unrecognized compensation cost $ 30,000,000          
Unrecognized compensation cost period of recognition (years) 1 year 6 months          
Fair value of shares vested $ 16,400,000 $ 19,500,000 $ 22,800,000      
Share-based payment expense $ 17,200,000 $ 15,100,000 $ 24,600,000      
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 | 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 | Stock options            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Unrecognized compensation cost $ 8,900,000          
Unrecognized compensation cost period of recognition (years) 1 year 8 months 12 days          
Stock options outstanding (in shares) 1,100,000 1,200,000 900,000     400,000
Award expiration term 10 years          
Intrinsic value of options exercised $ 14,000,000 $ 1,200,000 $ 0      
Total intrinsic value of stock options outstanding 40,600,000          
Total intrinsic value of stock options expected to vest 18,800,000          
Total intrinsic value of stock options exercisable 21,400,000          
Share-based payment expense $ 8,800,000 9,200,000 4,900,000      
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | 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) 700,000          
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) 400,000          
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Performance stock units            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Share-based compensation vesting period (years) 3 years          
Unrecognized compensation cost $ 9,000,000          
Unrecognized compensation cost period of recognition (years) 1 year 6 months          
Performance stock units outstanding 200,000          
Share-based payment expense $ 9,900,000 6,800,000 7,300,000      
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | 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      
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) 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%