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Stock-Based Compensation Plans (Narrative) (Details) $ in Thousands |  |  | 12 Months Ended
--- | --- | --- | ---
Jan. 14, 2022 shares | Oct. 02, 2020 USD ($) item | Aug. 31, 2024 USD ($) item shares | Aug. 31, 2023 USD ($) item shares | Aug. 31, 2022 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Capitalized stock-based compensation expense |  |  | $ 0 | $ 0 | $ 0
Common stock issued from treasury stock | shares |  |  | 666,440 |  |
Shares withheld for tax | shares |  |  | 251,686 | 17,639 | 86,125
Shares withheld for tax, fair value |  |  | $ 10,300 |  |
Compensation cost |  |  | 10,142 | $ 12,520 | $ 8,286
Fiscal 2021 Acquisition Of Strive Talent Plan [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Compensation cost |  |  | $ 2,200 |  |
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 |  |
Contingent consideration period |  |  | 5 years |  |
Common Stock [Member] | Omnibus Incentive Plan [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Shares reserved for payment of consideration | shares |  |  | 200,000 |  |
Performance Award [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Unrecognized compensation expense |  |  | $ 13,100 |  |
Weighted-average vesting period for recognition |  |  | 1 year 7 months 6 days |  |
Service period |  | 2 years |  |  |
Compensation cost |  |  | $ 8,275 | $ 10,767 | $ 6,133
Increase adjusted EBITDA vesting target |  | $ 2,000 |  |  |
Number of impacted associates apart of compensation plan modification | item |  | 20 |  |  |
Number of individuals who qualified for award | item |  |  | 5 | 3 | 3
Performance Award [Member] | Omnibus Incentive 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 |  |  | 307,000 |  |
Employee Stock Purchase Plan [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Compensation cost |  |  | $ 252 | $ 269 | $ 239
Price of common stock as a percent of the average fair market value |  |  | 85.00% |  |
Shares issued to employee stock purchase plan participants | shares |  |  | 44,040 | 40,141 | 36,960
Proceeds from Issuance of Shares under Incentive and Share-based Compensation Plans, Excluding Stock Options |  |  | $ 1,500 |  | $ 1,300
Cost basis of shares issued to employee stock purchase plan participants |  |  | $ 800 | $ 700 | 600
Employee Stock Purchase Plan [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 |  |  | 689,000 |  |
Unvested Stock Awards [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Unrecognized compensation expense |  |  | $ 300 |  |
Weighted-average vesting period for recognition |  |  | 4 months |  |
Vesting period of awards |  |  | 1 year |  |
Compensation cost |  |  | $ 880 | 700 | 673
Intrinsic value of unvested stock awards |  |  | 900 |  |
Whole-share grant per eligible director |  |  | 120 |  |
Total recognized tax benefit from unvested stock awards |  |  | 200 | 200 | 200
Issuance of common stock from treasury |  |  | 400 | 300 | 200
Unvested Stock Awards [Member] | Board Of Directors [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Fair value of shares awarded |  |  | $ 1,000 | $ 700 | $ 700
Shares issued under terms of the award | shares |  |  | 23,136 | 15,882 | 13,260
Long-Term Incentive Plans [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Number of tranches | item |  |  | 2 |  |
Vesting period of awards |  |  | 3 years |  |
Measurement period |  |  | 3 years |  |
Long-Term Incentive Plans [Member] | Tranche One [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Percent of award shares vest |  |  | 100.00% |  |
Long-Term Incentive Plans [Member] | Minimum [Member] | Tranche One [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Percent of award shares vest |  |  | 50.00% |  |
Long-Term Incentive Plans [Member] | Maximum [Member] | Tranche One [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Percent of award shares vest |  |  | 200.00% |  |
Long-Term Incentive And Retention Equity Awards [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |
Vesting period of awards |  |  | 3 years |  |
Percent of shares which will vest |  |  | 33.33% |  |
Shares issued under terms of the award | shares |  |  | 48,740 | 40,009 |

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