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Earnings per Common Share (Schedule of Reconciliation of Net Income to Net Income Available to Common Shareholders) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Earnings Per Share [Abstract]      
Net income $ 65,993 $ 67,329 $ 70,229
Less: Net income allocated to participating securities (272) (251) (277)
Net income available to common stockholders, basic 65,721 67,078 69,952
Net income available to common stockholders, diluted $ 65,721 $ 67,078 $ 69,952