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Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands | 3 Months Ended | 9 Months Ended
--- | --- | ---
May 27, 2023 | Feb. 25, 2023 | Nov. 26, 2022 | May 28, 2022 | Feb. 26, 2022 | Nov. 27, 2021 | May 27, 2023 | May 28, 2022
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |  |  |  |  |  |  |
Net income available to shareholders | $ 24,276 | $ 17,810 | $ 33,957 | $ 25,067 | $ 18,451 | $ 33,705 | $ 76,043 | $ 77,223
Allocation of net income for Basic: |  |  |  |  |  |  |  |
Common Stock | $ 24,276 |  |  | $ 25,067 |  |  | $ 76,043 | $ 77,223
Weighted average number of shares for Basic: |  |  |  |  |  |  |  |
Common stock (in shares) | 18,677 |  |  | 18,802 |  |  | 18,674 | 18,843
Common Stock |  |  |  |  |  |  |  |
Allocation of net income for Basic: |  |  |  |  |  |  |  |
Common Stock | $ 20,394 |  |  | $ 21,037 |  |  | $ 63,882 | $ 64,835
Weighted average number of shares for Basic: |  |  |  |  |  |  |  |
Common stock (in shares) | 15,087 |  |  | 15,170 |  |  | 15,084 | 15,211
Income per share for Basic: |  |  |  |  |  |  |  |
Common stock (in dollars per share) | $ 1.35 |  |  | $ 1.39 |  |  | $ 4.23 | $ 4.26
Class B Common Stock |  |  |  |  |  |  |  |
Allocation of net income for Basic: |  |  |  |  |  |  |  |
Common Stock | $ 3,882 |  |  | $ 4,030 |  |  | $ 12,161 | $ 12,388
Weighted average number of shares for Basic: |  |  |  |  |  |  |  |
Common stock (in shares) | 3,590 |  |  | 3,632 |  |  | 3,590 | 3,632
Income per share for Basic: |  |  |  |  |  |  |  |
Common stock (in dollars per share) | $ 1.08 |  |  | $ 1.11 |  |  | $ 3.39 | $ 3.41

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