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Share-Based Compensation (Summary of Restricted Stock Unit Activity) (Details) - Restricted Stock Units [Member]
12 Months Ended
Aug. 31, 2021
$ / shares
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Stock units outstanding | shares 72,723
Granted, number of stock units | shares 32,880
Vested, number of stock units | shares (44,252)
Forfeited/ cancelled, number of stock units | shares (4,011)
Stock units outstanding | shares 57,340
Stock units, weighted-average grant-date fair value | $ / shares $ 89.92
Granted, weighted-average grant-date fair value | $ / shares 111.96
Vested, weighted-average grant-date fair value | $ / shares 89.30
Forfeited/ cancelled, weighted-average grant-date fair value | $ / shares 96.73
Stock units, weighted-average grant-date fair value | $ / shares $ 102.60