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Stockholders' Equity - Share Repurchases (Details) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Feb. 28, 2023
Feb. 28, 2022
Feb. 28, 2023
Feb. 28, 2022
Equity [Abstract]        
Repurchase of common stock (in shares) 0 0 0 46,200
Repurchases of common stock $ 0 $ 0 $ 0 $ 18,639
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Remaining authorized repurchase amount $ 181,300   $ 181,300  
Restricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares repurchased from employees (in shares) 1,853 675 27,713 7,422
Value of shares repurchased in settlement of employee tax withholding obligations $ 800 $ 300 $ 11,800 $ 3,300