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. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 103,674	$ 103,404	$ 151,111
Allocation of net income for Basic:
Common stock	$ 103,674	$ 103,404	$ 151,111
Weighted average number of shares for Basic:
Common stock (in shares)	18,688	18,824	18,880
Common Stock
Allocation of net income for Basic:
Common stock	$ 87,104	$ 86,844	$ 126,848
Weighted average number of shares for Basic:
Common stock (in shares)	15,098	15,203	15,237
Income per share for Basic:
Common stock (in dollars per share)	$ 5.77	$ 5.71	$ 8.32
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 16,570	$ 16,560	$ 24,263
Weighted average number of shares for Basic:
Common stock (in shares)	3,590	3,621	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 4.62	$ 4.57	$ 6.66