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. 29, 2026	Aug. 30, 2025	Aug. 31, 2024
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 109,490	$ 148,271	$ 145,474
Allocation of net income for Basic:
Common stock	$ 109,490	$ 148,271	$ 145,474
Weighted average number of shares for Basic:
Common stock (in shares)	18,096	18,521	18,663
Common Stock
Allocation of net income for Basic:
Common stock	$ 91,595	$ 124,551	$ 122,188
Weighted average number of shares for Basic:
Common stock (in shares)	14,545	14,961	15,073
Income per share for Basic:
Common stock (in dollars per share)	$ 6.30	$ 8.33	$ 8.11
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 17,895	$ 23,720	$ 23,286
Weighted average number of shares for Basic:
Common stock (in shares)	3,551	3,560	3,590
Income per share for Basic:
Common stock (in dollars per share)	$ 5.04	$ 6.66	$ 6.49