Stock-Based Compensation (Narrative) (Details)	3 Months Ended	6 Months Ended
Feb. 29, 2024 shares	Feb. 29, 2024 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock issued from treasury stock	32,967	633,684
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Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
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Cumulative adjustment reduction to stock-based compensation expense \| $		$ 1,600,000
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Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period of awards		3 years
Shares issued under terms of the award		48,740
Time-Based Award [Member] \| Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		25.00%
Shares may be awarded		26,749
Number of tranches \| item		1
Performance Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares issued under terms of the award		80,217
Performance Award [Member] \| Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
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Vesting period of awards		3 years
Percent of performance-based objectives	100.00%	100.00%
Employee Stock Purchase Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Price of common stock as a percent of the average fair market value		85.00%
Shares issued to employee stock purchase plan participants	9,831	19,528
Unvested Stock Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period of awards		1 year
Whole-share grant per eligible director \| $		$ 120,000
Vest August 31 Of Each Year Following Grant [Member] \| Annual Long-Term Incentive Performance And Retention Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of award shares vest		33.30%
Tranche One and Two [Member] \| Performance Award [Member] \| Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares may be awarded		160,434
Tranche One and Two [Member] \| Performance Award [Member] \| Minimum [Member] \| Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		50.00%
Tranche One and Two [Member] \| Performance Award [Member] \| Maximum [Member] \| Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		200.00%

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