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. 28, 2021	Aug. 29, 2020	Aug. 31, 2019
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 151,111	$ 135,770	$ 179,134
Allocation of net income for Basic:
Common stock	$ 151,111	$ 135,770	$ 179,134
Weighted average number of shares for Basic:
Common stock (in shares)	18,880	18,919	19,082
Common Stock
Allocation of net income for Basic:
Common stock	$ 126,848	$ 114,017	$ 150,247
Weighted average number of shares for Basic:
Common stock (in shares)	15,237	15,276	15,385
Income per share for Basic:
Common stock (in dollars per share)	$ 8.32	$ 7.46	$ 9.77
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 24,263	$ 21,753	$ 28,887
Weighted average number of shares for Basic:
Common stock (in shares)	3,643	3,643	3,697
Income per share for Basic:
Common stock (in dollars per share)	$ 6.66	$ 5.97	$ 7.81