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Stock Based Compensation - Narrative (Details) - USD ($)
3 Months Ended 6 Months Ended
Jan. 17, 2023
Nov. 01, 2022
Nov. 01, 2021
Feb. 28, 2023
Feb. 28, 2022
Feb. 28, 2023
Feb. 28, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Stock-based compensation expense       $ 15,300,000 $ 15,500,000 $ 27,500,000 $ 25,900,000
Unrecognized compensation expense related to non-vested equity       $ 139,700,000   $ 139,700,000  
Weighted average period for recognition           3 years 2 months 12 days  
Employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Number of shares available for grant (in shares)       4,200,000   4,200,000  
Stock options granted (in shares)   266,051 292,377     267,641 302,493
Non-employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Number of shares available for grant (in shares)       200,000   200,000  
Stock options granted (in shares) 5,462            
PSUs | Minimum              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Payout percentage   0.00% 0.00%        
PSUs | Maximum              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Payout percentage   150.00% 150.00%        
PSUs | Employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted (in shares)           34,482 30,704
ESPP              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Stock-based compensation expense       $ 600,000 $ 500,000 $ 1,300,000 $ 1,100,000
Offering period           3 months  
Purchase price percentage           85.00%  
Maximum employee subscription rate       10.00%   10.00%  
Maximum contribution limit           $ 25,000  
Required holding period           18 months  
Capital shares reserved for future issuance (in shares)       84,576   84,576  
RSUs | Employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Vesting percentage   20.00% 20.00%        
Granted (in shares)           47,371 59,738
RSUs | Non-employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Vesting percentage 100.00%            
Granted (in shares) 1,653            
Weighted average grant date fair value (in USD per share) $ 425.06            
Stock options | Employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Vesting percentage   20.00% 20.00%        
Expiration period   10 years 10 years        
Stock options | Non-employee              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Vesting percentage 100.00%            
Expiration period 7 years