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. 30, 2025	Aug. 31, 2024	Aug. 26, 2023
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 148,271	$ 145,474	$ 103,674
As reported - Basic (in shares)	18,521	18,663	18,688
Common Stock	$ 148,271	$ 145,474	$ 103,674
Common stock (in shares)	18,581	18,724	18,762
Diluted Income Per Share - Common Stock (in dollars per share)	$ 7.98	$ 7.77	$ 5.53
Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 124,551	$ 122,188	$ 87,104
As reported - Basic (in shares)	14,961	15,073	15,098
As reported - Basic (in dollars per share)	$ 8.33	$ 8.11	$ 5.77
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	60	61	74
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported—Basic	$ 23,720	$ 23,286	$ 16,570
As reported - Basic (in shares)	3,560	3,590	3,590
As reported - Basic (in dollars per share)	$ 6.66	$ 6.49	$ 4.62