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Share-based Compensation - Summary of Performance-based Awards Activity (Details) - Performance Shares (PSUs) - $ / shares
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Number of Shares:      
Outstanding, Beginning Balance (in shares) 873,000    
Granted (in shares) 153,080 316,649 337,770
Performance achievement (in shares) 61,000    
Vested (in shares) (263,000)    
Forfeited (in shares) (42,000)    
Outstanding, Ending Balance (in shares) 782,000 873,000  
Weighted Average Grant Date Fair Value:      
Nonvested, Weighted Average Grant Date Fair Value, Beginning Balance $ 23.62    
Granted, Weighted Average Grant Date Fair Value 54.29 $ 22.33 $ 21.32
Performance achievement, Weighted Average Grant Date Fair Value 29.17    
Vested, Weighted Average Grant Date Fair Value 28.66    
Forfeited, Weighted Average Grant Date Fair Value 27.44    
Nonvested, Weighted Average Grant Date Fair Value, Ending Balance $ 28.16 $ 23.62