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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. 28, 2021 | Aug. 29, 2020 | Aug. 31, 2019
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |  |
Net income available to shareholders | $ 151,111 | $ 135,770 | $ 179,134
Allocation of net income for Basic: |  |  |
Common stock | $ 151,111 | $ 135,770 | $ 179,134
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 18,880 | 18,919 | 19,082
Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 126,848 | $ 114,017 | $ 150,247
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 15,237 | 15,276 | 15,385
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 8.32 | $ 7.46 | $ 9.77
Class B Common Stock |  |  |
Allocation of net income for Basic: |  |  |
Common stock | $ 24,263 | $ 21,753 | $ 28,887
Weighted average number of shares for Basic: |  |  |
Common stock (in shares) | 3,643 | 3,643 | 3,697
Income per share for Basic: |  |  |
Common stock (in dollars per share) | $ 6.66 | $ 5.97 | $ 7.81

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