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 28, 2022	Feb. 26, 2022	Nov. 27, 2021	May 29, 2021	Feb. 27, 2021	Nov. 28, 2020	May 28, 2022	May 29, 2021
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 25,067	$ 18,451	$ 33,705	$ 42,016	$ 32,585	$ 41,896	$ 77,223	$ 116,497
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 25,067			$ 42,016			$ 77,223	$ 116,497
Weighted average number of shares for Basic:
Common stock (in shares)	18,802			18,881			18,843	18,881
Common Stock
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 21,037			$ 35,270			$ 64,835	$ 97,792
Weighted average number of shares for Basic:
Common stock (in shares)	15,170			15,238			15,211	15,238
Income per share for Basic:
Common stock (in dollars per share)	$ 1.39			$ 2.31			$ 4.26	$ 6.42
Class B Common Stock
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 4,030			$ 6,746			$ 12,388	$ 18,705
Weighted average number of shares for Basic:
Common stock (in shares)	3,632			3,643			3,632	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 1.11			$ 1.85			$ 3.41	$ 5.13