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Stock Based Compensation - Narrative (Details) - USD ($)
3 Months Ended 9 Months Ended
Jan. 18, 2022
Nov. 01, 2021
May 31, 2022
May 31, 2021
May 31, 2022
May 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock-based compensation expense     $ 14,700,000 $ 11,000,000.0 $ 40,600,000 $ 33,400,000
Unrecognized compensation expense related to non-vested equity     $ 121,100,000   $ 121,100,000  
Weighted average period for recognition         3 years 1 month 6 days  
Stock options granted (in shares)         302,952  
Exercise price (in USD per share)         $ 434.64  
Number of shares available for grant (in shares)     4,700,000   4,700,000  
Number of share purchased by employees (in shares)     9,904 10,621 27,321 29,418
Stock issued during period employee stock purchase plans weighted average price per share (in USD per share)     $ 328.85 $ 267.02 $ 336.22 $ 271.94
Non-employee            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares) 6,329          
Stock options            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Exercise price (in USD per share)   $ 434.82        
Award vesting percentage   20.00%        
Award vesting period   5 years        
Expiration period   10 years        
Stock options | Non-employee            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Exercise price (in USD per share) $ 428.71          
Award vesting percentage         100.00%  
Award vesting period         3 years  
Expiration period         7 years  
Number of shares available for grant (in shares)     227,348   227,348  
Restricted stock units and performance-based awards            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Weighted average grant date fair value (in USD per share)         $ 418.16  
Restricted stock units            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting percentage   20.00%        
Award vesting period   5 years     3 years  
Non-option award grants (in shares)         71,933  
Restricted stock units | Non-employee            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting percentage 100.00%          
Non-option award grants (in shares) 1,629          
Weighted average grant date fair value (in USD per share) $ 425.49          
Performance-based awards            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting period         3 years  
Non-option award grants (in shares)         30,704  
ESPP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock-based compensation expense     $ 600,000 $ 500,000 $ 1,700,000 $ 1,500,000
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)     111,635   111,635