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. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 103,404	$ 151,111	$ 135,770
As reported - Basic (in shares)	18,824	18,880	18,919
Common Stock	$ 103,404	$ 151,111	$ 135,770
Common stock (in shares)	18,933	19,038	19,042
Diluted Income Per Share - Common Stock (in dollars per share)	$ 5.46	$ 7.94	$ 7.13
Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 86,844	$ 126,848	$ 114,017
As reported - Basic (in shares)	15,203	15,237	15,276
As reported - Basic (in dollars per share)	$ 5.71	$ 8.32	$ 7.46
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	109	158	123
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 16,560	$ 24,263	$ 21,753
As reported - Basic (in shares)	3,621	3,643	3,643
As reported - Basic (in dollars per share)	$ 4.57	$ 6.66	$ 5.97