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Stock-Based Compensation Plans (Narrative) (Details) $ in Thousands							3 Months Ended	12 Months Ended
	Oct. 14, 2022 shares	Feb. 04, 2022 shares	Jan. 14, 2022 shares	Oct. 02, 2020 USD ($) shares	Oct. 18, 2019 item shares	Oct. 01, 2018 item shares	Nov. 30, 2023 shares	Aug. 31, 2023 USD ($) item shares	Aug. 31, 2022 USD ($) item shares	Aug. 31, 2021 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock issued from treasury stock \| shares								114,214
Shares withheld for tax \| shares								17,639
Shares withheld for tax, fair value								$ 800
Capitalized stock-based compensation expense								0
Compensation cost								$ 12,520	$ 8,286	$ 8,617
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								33.33%
Number of tranches \| item								2
Vesting period of awards								3 years
Shares issued under terms of the award \| shares								40,009
Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item								2
Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item									2
Fiscal 2021 Acquisition Of Strive Talent Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Compensation cost								$ 1,500
Fiscal 2021 Acquisition Of Strive Talent Plan [Member] \| Bonus [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period								18 months
Compensation								$ 1,000
Compensation cost								800
Former Principal Owner [Member] \| Fiscal 2021 Acquisition Of Strive Talent Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Compensation								$ 4,200
Trading days								15 days
Shares required to be distributed within, days								45 days
Common Stock [Member] \| 2022 Omnibus Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares reserved for payment of consideration \| shares								200,000
Stock Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock options exercised \| shares									218,750
Shares withheld for tax \| shares									51,738
Shares withheld for tax, fair value									$ 1,300
Intrinsic value of the exercised options									2,900
Income tax benefit from exercise of the options									700
Income tax benefit upon exercise of the options									500
Unvested Stock Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense								$ 200
Whole-share grant per eligible director								$ 120
Vesting period of awards								1 year
Weighted-average vesting period for recognition								4 months
Total recognized tax benefit from unvested stock awards								$ 200	200	200
Intrinsic value of unvested stock awards								700
Compensation cost								700	673	700
Issuance of common stock from treasury								300	200	400
Unvested Stock Awards [Member] \| Board Of Directors [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Fair value of shares awarded								$ 700	$ 700	$ 700
Shares issued under terms of the award \| shares								15,882	13,260	28,049
Time-Based Award [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares authorized to be issued \| shares					23,701
Time-Based Award [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares authorized to be issued \| shares						34,605
Performance Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period				2 years
Increase Adjusted EBITDA vesting target				$ 2,000
Unrecognized compensation expense								$ 11,100
Number of individuals who qualified for award \| item								3	3	4
Compensation cost								$ 10,767	$ 6,133	$ 7,298
Performance 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								100.00%
Vesting period of awards	3 years
Shares issued under terms of the award \| shares								80,018
Performance Award [Member] \| 2022 Omnibus Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Authorized additional shares of common stock for issuance \| shares			1,000,000
Shares available for future grants \| shares								594,000
Performance Award [Member] \| Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period of awards		3 years
Performance Award [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period of awards				3 years
Performance Award [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Increase Adjusted EBITDA vesting target								$ 2,000
Shares authorized to be issued \| shares					141,154
Number of tranches \| item					3
Life of awards					3 years
Expiration date								Aug. 31, 2024
Percent of shares plan participants are entitled to					25.00%
Vesting period of awards					3 years
Percent of performance-based objectives					100.00%
Shares issued under terms of the award \| shares					70,577
Performance Award [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period								2 years
Increase Adjusted EBITDA vesting target								$ 2,000
Number of tranches \| item						3
Life of awards						3 years
Expiration date								Aug. 31, 2023
Percent of shares plan participants are entitled to						25.00%
Vesting period of awards						3 years
ESPP [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 \| shares								40,141	36,960	51,581
Cost basis of shares issued to employee stock purchase plan participants								$ 700	$ 600	$ 800
Proceeds from ESPP participants								1,500	1,300	1,100
Compensation cost								$ 269	$ 239	$ 205
ESPP [Member] \| 2017 Employee Stock Purchase Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares remaining in employee stock purchase plan \| shares								733,000
Tranche One and Two [Member] \| Performance 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 \| shares								160,036
Tranche One and Two [Member] \| Performance 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 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%
Tranche One [Member] \| 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%
Vesting period of awards	3 years
Shares issued under terms of the award \| shares	26,682
Tranche One [Member] \| Time-Based Award [Member] \| Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of award shares vest		25.00%
Shares issued under terms of the award \| shares		24,138
Tranche One [Member] \| Time-Based Award [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of award shares vest				25.00%
Shares issued under terms of the award \| shares				51,617
Tranche Two and Three [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item					2
Tranche Two and Three [Member] \| Performance Award [Member] \| Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance-based objectives		100.00%
Shares issued under terms of the award \| shares		72,397
Tranche Two and Three [Member] \| Performance Award [Member] \| Minimum [Member] \| Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		50.00%
Tranche Two and Three [Member] \| Performance Award [Member] \| Minimum [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted					50.00%
Tranche Two and Three [Member] \| Performance Award [Member] \| Maximum [Member] \| Fiscal 2022 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		200.00%
Shares may be awarded \| shares		144,794
Tranche Two and Three [Member] \| Performance Award [Member] \| Maximum [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted					200.00%
Scenario, Forecast [Member] \| Performance Award [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares authorized to be issued \| shares							204,418
Scenario, Forecast [Member] \| Tranche One and Two [Member] \| Performance Award [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares issued under terms of the award \| shares							309,660