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 25, 2024	Feb. 24, 2024	Nov. 25, 2023	May 27, 2023	Feb. 25, 2023	Nov. 26, 2022	May 25, 2024	May 27, 2023
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 38,057	$ 20,457	$ 42,325	$ 24,276	$ 17,810	$ 33,957	$ 100,839	$ 76,043
Allocation of net income for Basic:
Common stock	$ 38,057			$ 24,276			$ 100,839	$ 76,043
Weighted average number of shares for Basic:
Common stock (in shares)	18,652			18,677			18,684	18,674
Common Stock
Allocation of net income for Basic:
Common stock	$ 31,962			$ 20,394			$ 84,716	$ 63,882
Weighted average number of shares for Basic:
Common stock (in shares)	15,062			15,087			15,094	15,084
Income per share for Basic:
Common stock (in dollars per share)	$ 2.12			$ 1.35			$ 5.61	$ 4.23
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 6,095			$ 3,882			$ 16,123	$ 12,161
Weighted average number of shares for Basic:
Common stock (in shares)	3,590			3,590			3,590	3,590
Income per share for Basic:
Common stock (in dollars per share)	$ 1.7			$ 1.08			$ 4.49	$ 3.39