Summary of Significant Accounting Policies - Schedule of Computation of Diluted 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 Diluted [Line Items]
As reported—Basic	$ 151,111	$ 135,770	$ 179,134
As reported - Basic (in shares)	18,880	18,919	19,082
Common Stock	$ 151,111	$ 135,770	$ 179,134
Common stock (in shares)	19,038	19,042	19,196
Diluted Income Per Share – Common Stock (in dollars per share)	$ 7.94	$ 7.13	$ 9.33
Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 126,848	$ 114,017	$ 150,247
As reported - Basic (in shares)	15,237	15,276	15,385
As reported - Basic (in dollars per share)	$ 8.32	$ 7.46	$ 9.77
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	158	123	114
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 24,263	$ 21,753	$ 28,887
As reported - Basic (in shares)	3,643	3,643	3,697
As reported - Basic (in dollars per share)	$ 6.66	$ 5.97	$ 7.81