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Employee and Non-employee Director Stock Option and Retirement Plans - Narrative (Details) - USD ($)
3 Months Ended 9 Months Ended
Jan. 15, 2020
Nov. 01, 2019
May 31, 2020
May 31, 2019
May 31, 2020
May 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Weighted average exercise price (in USD per share)   $ 255.87        
Purchase price (in percentage)         85.00%  
Maximum employee subscription rate (in percentage)     10.00%   10.00%  
Maximum contribution limit         $ 25,000  
Number of share purchased by employees (in shares)     11,084 13,350 33,735 39,069
Stock issued during period employee stock purchase plans weighted average price per share (in USD per share)     $ 238.81 $ 201.54 $ 226.79 $ 199.43
Capital shares reserved for future issuance (in shares)     186,675   186,675  
Stock-based compensation expense     $ 10,300,000 $ 8,000,000.0 $ 28,400,000 $ 24,100,000
Unrecognized compensation expense related to non-vested equity     $ 89,100,000   $ 89,100,000  
LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)         422,346  
Weighted average exercise price (in USD per share)         $ 256.05  
Number of shares available for grant (in shares)     5,600,000   5,600,000  
Director Plan            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Number of shares available for grant (in shares)     247,876   247,876  
Director Plan | Non-employee | Directors            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares) 16,080          
Award vesting period 3 years          
Expiration period 7 years          
Weighted average grant date fair value (in USD per share) $ 54.74          
ESPP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock-based compensation expense     $ 600,000 $ 600,000 $ 1,600,000 $ 1,600,000
Weighted average period for recognition     3 years 1 month 6 days      
Stock options | LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)   412,098        
Award vesting (in percentage)   20.00%        
Award vesting period   5 years        
Stock options | LTIP | Maximum            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Expiration period   10 years        
RSUs            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Non-option award grants (in shares)         30,766  
RSUs | LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)         29,817  
Award vesting period         5 years  
Weighted average grant date fair value (in USD per share)         $ 245.48  
RSUs | LTIP | Maximum            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting (in percentage)         20.00%  
PRSUs            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Non-option award grants (in shares)         36,909  
PRSUs | LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)         36,501  
Award vesting period         3 years