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Share Repurchases (Narrative) (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Equity [Abstract]      
Repurchase authorization amount $ 250.0    
Number of shares of common stock repurchased during the period 0 0 0
Remaining amount available under the repurchase program $ 63.7