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Stock-Based Compensation Plans - Narrative (Details) - USD ($) $ / shares in Units, $ in Thousands |  | 12 Months Ended |
--- | --- | --- | ---
Oct. 12, 2021 | Aug. 27, 2022 | Aug. 28, 2021 | Aug. 29, 2020 | Aug. 31, 2019 | Dec. 11, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Accrued compensation |  |  | $ 67,541 | $ 36,533 |  |
Unrecognized compensation expense related to stock options |  |  | $ 1,226 |  |  |
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 |  |  | $ 3,804 |  |  |
Unrecognized compensation expense, period of recognition |  |  | 1 year |  |  |
Total fair value of awards vested |  |  | $ 1,445 | $ 2,438 |  |
Granted (in shares) |  |  | 97,996 |  |  |
Vested (in shares) |  |  | 26,515 | 0 | 0 |
Time-based |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Unrecognized compensation expense |  |  | $ 7,122 |  |  |
Unrecognized compensation expense, period of recognition |  |  | 9 months 18 days |  |  |
Total fair value of awards vested |  |  | $ 5,210 | $ 3,324 | $ 6,648 |
Granted (in shares) |  |  | 150,275 |  |  |
Vested (in shares) |  |  | 92,942 |  |  |
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] |  |  |  |  |  |
Discount market price percentage |  |  | 15.00% |  |  |
Term of sale restriction period after grant |  |  | 1 year |  |  |
Shares purchased through the ESPP (in shares) |  |  | 24,000 | 21,000 |  |
Accrued compensation |  |  | $ 385 | $ 274 |  |
Restricted Stock Units (RSUs) | Key Management | Subsequent Event |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) | 124,978 |  |  |  |  |
Shares granted, value | $ 9,447 |  |  |  |  |
Closing price of common stock on grant date (in dollars per share) | $ 75.59 |  |  |  |  |
Restricted Stock Units (RSUs) | Key Management | Scenario, Forecast | Subsequent Event |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Stock-based compensation expense |  | $ 3,149 |  |  |  |
Incentive Compensation Plan 2019 |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares authorized (in shares) |  |  |  |  |  | 4,100,000

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