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. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 103,404	$ 151,111	$ 135,770
Allocation of net income for Basic:
Common stock	$ 103,404	$ 151,111	$ 135,770
Weighted average number of shares for Basic:
Common stock (in shares)	18,824	18,880	18,919
Common Stock
Allocation of net income for Basic:
Common stock	$ 86,844	$ 126,848	$ 114,017
Weighted average number of shares for Basic:
Common stock (in shares)	15,203	15,237	15,276
Income per share for Basic:
Common stock (in dollars per share)	$ 5.71	$ 8.32	$ 7.46
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 16,560	$ 24,263	$ 21,753
Weighted average number of shares for Basic:
Common stock (in shares)	3,621	3,643	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 4.57	$ 6.66	$ 5.97