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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. 31, 2024 | Aug. 26, 2023 | Aug. 27, 2022
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |  |
Net income | $ 145,474 | $ 103,674 | $ 103,404
Allocation of net income for Basic: |  |  |
Common stock | $ 145,474 | $ 103,674 | $ 103,404
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 18,663 | 18,688 | 18,824
Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 122,188 | $ 87,104 | $ 86,844
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 15,073 | 15,098 | 15,203
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 8.11 | $ 5.77 | $ 5.71
Class B Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 23,286 | $ 16,570 | $ 16,560
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 3,590 | 3,590 | 3,621
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 6.49 | $ 4.62 | $ 4.57

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