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