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Share-Based Compensation (Summary of Restricted Stock Unit Activity) (Details) - Restricted Stock Units [Member]
12 Months Ended
Aug. 31, 2025
$ / shares
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Stock units outstanding | shares 52,581
Granted, number of stock units | shares 39,067
Vested, number of stock units | shares (22,349)
Forfeited/ cancelled, number of stock units | shares (2,861)
Stock units outstanding | shares 66,438
Stock units, weighted-average grant-date fair value | $ / shares $ 131.12
Granted, weighted-average grant-date fair value | $ / shares 119.49
Vested, weighted-average grant-date fair value | $ / shares 133.54
Forfeited/ cancelled, weighted-average grant-date fair value | $ / shares 123.96
Stock units, weighted-average grant-date fair value | $ / shares $ 123.63