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Stock-based Compensation (Schedule of Restricted Stock Units Activity) (Details) - Restricted Stock Units - USD ($)
$ / shares in Units, $ in Thousands
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Number of Units      
Beginning Outstanding (in shares) 78,604    
Granted (in shares) 23,732    
Converted to shares of common stock (in shares) (22,032)    
Forfeited (in shares) (488)    
Ending Outstanding (in shares) 79,816 78,604  
Vested (in shares) 50,319    
Weighted-Average Grant Date Fair Value Per Unit      
Beginning Outstanding (in dollars per share) $ 148.28    
Granted (in dollars per share) 167.05 $ 217.03 $ 208.29
Converted to shares of common stock (in dollars per share) 182.16    
Forfeited (in dollars per share) 192.24    
Ending Outstanding (in dollar par share) 144.24 $ 148.28  
Vested (in dollars per share) $ 118.94    
Outstanding, Aggregate Intrinsic Value $ 17,150    
Vested, Aggregate Intrinsic Value $ 10,812