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Share Repurchase Plan (Details) - USD ($)
$ / shares in Units, $ in Thousands
12 Months Ended 22 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2023
Jun. 19, 2023
Oct. 12, 2021
Equity [Abstract]            
Share buy-back plan, amount authorized         $ 50,000 $ 75,000
Number of shares repurchased (in shares) 55,920     194,482    
Average price of shares repurchased (in dollars per share) $ 186.09     $ 203.42    
Payment for repurchased shares $ 10,434 $ 29,156 $ 0 $ 39,600