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Goodwill and Other Intangible Assets (Summary of Definite-Lived Intangible Assets) (Details) - USD ($)
$ in Thousands
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Goodwill and Intangible Assets Disclosure [Abstract]      
Gross carrying amount $ 35,877 $ 35,166  
Accumulated amortization (31,207) (29,578)  
Net carrying amount $ 4,670 $ 5,588 $ 7,244