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. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 103,674	$ 103,404	$ 151,111
As reported - Basic (in shares)	18,688	18,824	18,880
Common Stock	$ 103,674	$ 103,404	$ 151,111
Common stock (in shares)	18,762	18,933	19,038
Diluted Income Per Share - Common Stock (in dollars per share)	$ 5.53	$ 5.46	$ 7.94
Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 87,104	$ 86,844	$ 126,848
As reported - Basic (in shares)	15,098	15,203	15,237
As reported - Basic (in dollars per share)	$ 5.77	$ 5.71	$ 8.32
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	74	109	158
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 16,570	$ 16,560	$ 24,263
As reported - Basic (in shares)	3,590	3,621	3,643
As reported - Basic (in dollars per share)	$ 4.62	$ 4.57	$ 6.66