Summary of Significant Accounting Policies - Schedule of Computation of Basic 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, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 148,271	$ 145,474	$ 103,674
Allocation of net income for Basic:
Common stock	$ 148,271	$ 145,474	$ 103,674
Weighted average number of shares for Basic:
Common stock (in shares)	18,521	18,663	18,688
Common Stock
Allocation of net income for Basic:
Common stock	$ 124,551	$ 122,188	$ 87,104
Weighted average number of shares for Basic:
Common stock (in shares)	14,961	15,073	15,098
Income per share for Basic:
Common stock (in dollars per share)	$ 8.33	$ 8.11	$ 5.77
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 23,720	$ 23,286	$ 16,570
Weighted average number of shares for Basic:
Common stock (in shares)	3,560	3,590	3,590
Income per share for Basic:
Common stock (in dollars per share)	$ 6.66	$ 6.49	$ 4.62