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Stock-Based Compensation Plans (Narrative) (Details) $ / shares in Units, $ in Thousands |  |  |  |  |  |  |  | 12 Months Ended
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Oct. 02, 2020 USD ($) item shares | Oct. 18, 2019 item shares | Jan. 25, 2019 USD ($) $ / shares shares | Oct. 01, 2018 item shares | Nov. 14, 2017 item shares | Oct. 18, 2016 item shares | Nov. 12, 2015 item shares | Aug. 31, 2021 USD ($) item shares | Aug. 31, 2020 USD ($) item shares | Aug. 31, 2019 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Common stock issued from treasury stock |  |  |  |  |  |  |  | 432,564 |  |
Shares withheld for tax |  |  |  |  |  |  |  | 147,092 |  |
Shares withheld for tax, fair value | $ |  |  |  |  |  |  |  | $ 3,000 |  |
Capitalized stock-based compensation expense | $ |  |  |  |  |  |  |  | $ 0 |  |
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] | Bonus [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Service period |  |  |  |  |  |  |  | 18 months |  |
Compensation | $ |  |  |  |  |  |  |  | $ 1,000 |  |
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] | 2019 Omnibus Plan [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Shares reserved for payment of consideration |  |  |  |  |  |  |  | 200,000 |  |
Stock Options [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Stock options exercised |  |  |  |  |  |  |  | 218,750 | 350,000 |
Shares withheld for tax |  |  |  |  |  |  |  | 51,738 | 102,656 |
Shares withheld for tax, fair value | $ |  |  |  |  |  |  |  | $ 1,300 | $ 3,600 |
Intrinsic value of the exercised options | $ |  |  |  |  |  |  |  | 2,900 | 8,000 |
Income tax benefit from exercise of the options | $ |  |  |  |  |  |  |  | 700 | 1,800 |
Income tax benefit upon exercise of the options | $ |  |  |  |  |  |  |  | 500 |  |
Restricted Stock Awards [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Unrecognized compensation expense | $ |  |  |  |  |  |  |  | 200 |  |
Whole-share grant per eligible director | $ |  |  |  |  |  |  |  | $ 100 |  |
Vesting period of awards |  |  |  |  |  |  |  | 1 year |  |
Cost of common stock issued from treasury | $ |  |  |  |  |  |  |  | $ 400 | 300 | $ 400
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 | $ |  |  |  |  |  |  |  | 1,200 |  |
Restricted 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 |  |  |  |  |  |  |  | 28,049 | 21,420 | 28,525
Time-Based Award [Member] | Fiscal 2019 Time Based Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Service period |  |  | 2 years |  |  |  |  |  |  |
Price per share | $ / shares |  |  | $ 24.54 |  |  |  |  |  |  |
Vesting period of awards |  |  | 2 years |  |  |  |  |  |  |
Fair value of shares awarded | $ |  |  | $ 300 |  |  |  |  |  |  |
Shares issued under terms of the award |  |  | 11,915 |  |  |  |  |  |  |
Performance-Based 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 individuals who qualified for award | item |  |  |  |  |  |  |  | 4 | 4 | 4
Performance-Based Award [Member] | 2019 Omnibus Plan [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Shares available for future grants |  |  |  |  |  |  |  | 8,500 |  |
Performance-Based Award [Member] | Fiscal 2020 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Shares may be awarded |  | 25,101 |  |  |  |  |  |  |  |
Increase Adjusted EBITDA vesting target | $ |  |  |  |  |  |  |  | $ 2,000 |  |
Shares authorized to be issued |  | 150,630 |  |  |  |  |  |  |  |
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 |  |  |  |  |  |  |  |
Performance-Based Award [Member] | Fiscal 2019 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Shares may be awarded |  |  |  | 36,470 |  |  |  |  |  |
Service period |  |  |  |  |  |  |  | 2 years |  |
Increase Adjusted EBITDA vesting target | $ |  |  |  |  |  |  |  | $ 2,000 |  |
Shares authorized to be issued |  |  |  | 218,818 |  |  |  |  |  |
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 |  |  |  |  |  |
Performance-Based Award [Member] | Fiscal 2018 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Number of tranches | item |  |  |  |  | 3 |  |  |  |  |
Life of awards |  |  |  |  | 3 years |  |  |  |  |
Shares earned by participants |  |  |  |  |  |  |  | 221,067 |  |
Performance-Based Award [Member] | Fiscal 2017 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Increase Adjusted EBITDA vesting target | $ |  |  |  |  |  |  |  | $ 2,000 |  |
Remaining unvested shares |  |  |  |  |  |  |  | 0 |  |
Shares authorized to be issued |  |  |  |  |  | 183,381 |  |  |  |
Number of individual vesting conditions | item |  |  |  |  |  | 6 |  |  |  |
Number of performance measures | item |  |  |  |  |  | 2 |  |  |  |
Life of awards |  |  |  |  |  | 6 years |  |  |  |
Expiration date |  |  |  |  |  | Aug. 31, 2022 |  | Aug. 31, 2024 |  |
Performance-Based Award [Member] | Fiscal 2016 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Increase Adjusted EBITDA vesting target | $ |  |  |  |  |  |  |  | $ 2,000 |  |
Remaining unvested shares |  |  |  |  |  |  |  | 0 |  |
Shares authorized to be issued |  |  |  |  |  |  | 231,276 |  |  |
Number of individual vesting conditions | item |  |  |  |  |  |  | 6 |  |  |
Number of performance measures | item |  |  |  |  |  |  | 2 |  |  |
Life of awards |  |  |  |  |  |  | 6 years |  |  |
Expiration date |  |  |  |  |  |  | Aug. 31, 2021 | Aug. 31, 2023 |  |
Performance-Based Award [Member] | Common Stock [Member] | 2019 Omnibus Plan [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Authorized additional shares of common stock for issuance |  |  | 700,000 |  |  |  |  |  |  |
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 |  |  |  |  |  |  |  | 51,581 | 41,409 | 43,073
Cost basis of shares issued to employee stock purchase plan participants | $ |  |  |  |  |  |  |  | $ 800 | $ 600 | $ 600
Proceeds from ESPP participants | $ |  |  |  |  |  |  |  | $ 1,100 | $ 1,000 | $ 1,000
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 |  |  |  |  |  |  |  | 810,000 |  |
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 | 52,696 |  |  |  |  |  |  |  |  |
Tranche One [Member] | Performance-Based Award [Member] | Fiscal 2018 Long Term Incentive Plan Award [Member] |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Shares may be awarded |  |  |  |  | 42,883 |  |  |  |  |
Percent of shares plan participants are entitled to |  |  |  |  | 25.00% |  |  |  |  |
Vesting period of awards |  |  |  |  | 3 years |  |  |  |  |
Tranche Two and Three [Member] | Performance-Based Award [Member] | Fiscal 2021 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 | 158,088 |  |  |  |  |  |  |  |  |
Tranche Two and Three [Member] | Performance-Based Award [Member] | Minimum [Member] | Fiscal 2021 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-Based 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-Based Award [Member] | Minimum [Member] | Fiscal 2019 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-Based Award [Member] | Maximum [Member] | Fiscal 2021 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 | 316,176 |  |  |  |  |  |  |  |  |
Tranche Two and Three [Member] | Performance-Based 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% |  |  |  |  |  |  |  |
Tranche Two and Three [Member] | Performance-Based Award [Member] | Maximum [Member] | Fiscal 2019 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% |  |  |  |  |  |

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