Stock-Based Compensation (Narrative) (Details)	3 Months Ended	9 Months Ended
May 31, 2023 shares	May 31, 2023 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock issued from treasury stock		97,468
Shares withheld for tax		18,000
Fiscal 2023, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of shares which will vest		33.30%
Number of tranches \| item		2
Shares issued under terms of the award		42,600
Unvested Stock Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Whole-share grant per eligible director \| $		$ 120,000
Vesting period of awards		1 year
Time-Based Award [Member] \| Fiscal 2023, 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		27,000
Number of tranches \| item		1
Performance-Based Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares issued under terms of the award		81,135
Performance-Based Award [Member] \| Fiscal 2023, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item		1
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	10,495	28,086
Tranche One and Two [Member] \| Performance-Based Award [Member] \| Fiscal 2023, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares may be awarded		162,270
Tranche One and Two [Member] \| Performance-Based Award [Member] \| Minimum [Member] \| Fiscal 2023, 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-Based Award [Member] \| Maximum [Member] \| Fiscal 2023, 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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