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Stock Based Compensation - Narrative (Details) - USD ($)
3 Months Ended
Nov. 01, 2022
Nov. 30, 2022
Nov. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock-based compensation expense   $ 12,200,000 $ 10,400,000
Unrecognized compensation expense related to non-vested equity   $ 153,600,000  
Weighted average period for recognition   3 years 4 months 24 days  
Employee      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of shares available for grant (in shares)   4,200,000  
Stock options granted (in shares) 266,051 267,296 299,702
PSUs | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Payout percentage   0.00%  
PSUs | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Payout percentage   150.00%  
ESPP      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock-based compensation expense   $ 700,000 $ 500,000
Offering period   3 months  
Purchase price percentage   85.00%  
Maximum employee subscription rate   10.00%  
Maximum contribution limit   $ 25,000  
Required holding period   18 months  
Capital shares reserved for future issuance (in shares)   93,853