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Stock-Based Compensation Plans - Expense Components (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 27, 2022 | Aug. 28, 2021 | Aug. 29, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total stock-based compensation expense | $ 17,085 | $ 15,347 | $ 6,475
Time-based |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total stock-based compensation expense | 7,540 | 5,737 | 4,287
Performance-based |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total stock-based compensation expense | 7,412 | 7,920 | 796
Stock options |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total stock-based compensation expense | 1,000 | 1,019 | 990
Other |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Total stock-based compensation expense | $ 1,133 | $ 671 | $ 402

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