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Summary of Significant Accounting Policies - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands | 12 Months Ended
--- | ---
Aug. 30, 2025 | Aug. 31, 2024 | Aug. 26, 2023
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |  |
Net income | $ 148,271 | $ 145,474 | $ 103,674
Allocation of net income for Basic: |  |  |
Common stock | $ 148,271 | $ 145,474 | $ 103,674
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 18,521 | 18,663 | 18,688
Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 124,551 | $ 122,188 | $ 87,104
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 14,961 | 15,073 | 15,098
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 8.33 | $ 8.11 | $ 5.77
Class B Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 23,720 | $ 23,286 | $ 16,570
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 3,560 | 3,590 | 3,590
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 6.66 | $ 6.49 | $ 4.62

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