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Stock-Based Compensation Plans (Narrative) (Details) $ in Thousands |  |  |  |  |  |  | 3 Months Ended | 12 Months Ended
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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 |  |  |

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