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Stock-Based Compensation Plans (Unvested Stock Award) (Details) - Unvested Stock Awards [Member]
12 Months Ended
Aug. 31, 2025
$ / shares
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Unvested stock awards, Number of Shares | shares 23,136
Granted, Number of Shares | shares 27,336
Forfeited, Number of Shares | shares
Vested, Number of Shares | shares (23,136)
Unvested stock awards, Number of Shares | shares 27,336
Restricted stock awards, Weighted-Average Grant Date Fair Value Per Share | $ / shares $ 41.50
Granted, Weighted-Average Grant Date Fair Value Per Share | $ / shares 35.12
Forfeited, Weighted-Average Grant Date Fair Value Per Share | $ / shares
Vested, Weighted-Average Grant Date Fair Value Per Share | $ / shares 41.50
Restricted stock awards, Weighted-Average Grant Date Fair Value Per Share | $ / shares $ 35.12