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Share-based Compensation - Summary of Performance-based Awards Activity (Details) - Performance Shares (PSUs) - $ / shares
12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Number of Shares:      
Outstanding, Beginning Balance (in shares) 782,000    
Granted (in shares) 211,046 153,080 316,649
Performance achievement (in shares) 171,000    
Vested (in shares) (487,000)    
Forfeited (in shares) (50,000)    
Outstanding, Ending Balance (in shares) 627,000 782,000  
Weighted Average Grant Date Fair Value:      
Nonvested, Weighted Average Grant Date Fair Value, Beginning Balance $ 28.16    
Granted, Weighted Average Grant Date Fair Value 32.1 $ 54.29 $ 22.33
Performance achievement, Weighted Average Grant Date Fair Value 20.98    
Vested, Weighted Average Grant Date Fair Value 21.2    
Forfeited, Weighted Average Grant Date Fair Value 34.2    
Nonvested, Weighted Average Grant Date Fair Value, Ending Balance $ 32.44 $ 28.16