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Leases (Supplemental Cash Flow) (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Leases [Abstract]    
Operating Lease, Payments $ 14,166 $ 15,240
Right-of-Use Asset Obtained in Exchange for Operating Lease Liability $ 4,584 $ 9,197