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Employee and Non-employee Director Stock Option and Retirement Plans - Narrative (Details) - USD ($)
3 Months Ended 6 Months Ended
Jan. 15, 2020
Nov. 01, 2019
Feb. 29, 2020
Feb. 28, 2019
Feb. 29, 2020
Feb. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Weighted average exercise price (in USD per share)   $ 255.87        
Estimated fair value (in USD per share) $ 271.51 $ 60.19        
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)     11,493 12,624 22,652 25,719
Stock issued during period employee stock purchase plans weighted average price per share (in USD per share)     $ 221.12 $ 199.36 $ 220.91 $ 198.33
Capital shares reserved for future issuance (in shares)     197,758   197,758  
Stock based compensation expense     $ 8,200,000 $ 7,700,000 $ 18,000,000.0 $ 16,100,000
Unrecognized compensation expense related to non-vested equity     98,500,000   98,500,000  
Shares repurchased from employees, amount capitalized     $ 0 0 $ 0 0
LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)         417,417  
Weighted average exercise price (in USD per share)         $ 255.95  
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          
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     $ 500,000 $ 500,000 $ 1,000,000.0 $ 1,000,000.0
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  
Restricted stock units            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Non-option award grants (in shares)         30,379  
Restricted stock units | 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  
Restricted stock units | LTIP | Maximum            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Award vesting (in percentage)         20.00%  
Performance-based restricted stock units            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Non-option award grants (in shares)         36,501  
Performance-based restricted stock units | LTIP            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock options granted (in shares)         36,501  
Award vesting period         3 years