Stock-Based Compensation (Narrative) (Details)	3 Months Ended
	Nov. 30, 2023 item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock issued from treasury stock	600,717
Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches | item	2
Annual Long-Term Incentive Performance And Retention Plan [Member]
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	28,272
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	84,784
Performance Award [Member] | Fiscal 2024, Long-Term Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches | item	1
Vesting period of awards	3 years
Percent of performance-based objectives	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	9,697
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	169,568
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%