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. 31, 2024	Aug. 26, 2023	Aug. 27, 2022
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 145,474	$ 103,674	$ 103,404
As reported - Basic (in shares)	18,663	18,688	18,824
Common Stock	$ 145,474	$ 103,674	$ 103,404
Common stock (in shares)	18,724	18,762	18,933
Diluted Income Per Share - Common Stock (in dollars per share)	$ 7.77	$ 5.53	$ 5.46
Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 122,188	$ 87,104	$ 86,844
As reported - Basic (in shares)	15,073	15,098	15,203
As reported - Basic (in dollars per share)	$ 8.11	$ 5.77	$ 5.71
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	61	74	109
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 23,286	$ 16,570	$ 16,560
As reported - Basic (in shares)	3,590	3,590	3,621
As reported - Basic (in dollars per share)	$ 6.49	$ 4.62	$ 4.57