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Stock-Based Compensation Plans - Narrative (Details) - USD ($) $ in Millions |  | 12 Months Ended
--- | --- | ---
Dec. 14, 2023 | Aug. 31, 2024 | Aug. 26, 2023 | Aug. 27, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Accrued compensation |  | $ 35.9 | $ 35.9 |
Unrecognized compensation expense related to stock options |  | $ 1.6 |  |
Stock options |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Outstanding options term |  | 10 years |  |
Vesting period |  | 3 years |  |
Unrecognized compensation expense, period of recognition |  | 9 months 18 days |  |
Performance-based |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
Unrecognized compensation expense |  | $ 5.0 |  |
Unrecognized compensation expense, period of recognition |  | 1 year 2 months 12 days |  |
Total fair value of awards vested |  | $ 4.5 | 7.6 | $ 5.8
Time-based |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Unrecognized compensation expense |  | $ 10.0 |  |
Unrecognized compensation expense, period of recognition |  | 9 months 18 days |  |
Total fair value of awards vested |  | $ 8.4 | $ 8.8 | $ 8.0
Time-based | Director |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 1 year |  |
ESPP |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Number of shares authorized (in shares) |  | 550,000 |  |
Shares remain available for future issuance (in shares) |  | 353,000 |  |
Discount market price percentage |  | 15.00% |  |
Shares purchased through the ESPP (in shares) |  | 47,000 | 29,000 |
Accrued compensation |  | $ 0.5 | $ 0.5 |
Incentive Compensation Plan 2019 |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Number of shares authorized (in shares) | 2,400,000 |  |  |
Counted against share reserve (in shares) | 2 |  |  |
Incentive Compensation Plan 2014 |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Shares remain available for future issuance (in shares) |  | 3,800,000 |  |

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