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. 31, 2024	Aug. 26, 2023	Aug. 27, 2022
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 145,474	$ 103,674	$ 103,404
Allocation of net income for Basic:
Common stock	$ 145,474	$ 103,674	$ 103,404
Weighted average number of shares for Basic:
Common stock (in shares)	18,663	18,688	18,824
Common Stock
Allocation of net income for Basic:
Common stock	$ 122,188	$ 87,104	$ 86,844
Weighted average number of shares for Basic:
Common stock (in shares)	15,073	15,098	15,203
Income per share for Basic:
Common stock (in dollars per share)	$ 8.11	$ 5.77	$ 5.71
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 23,286	$ 16,570	$ 16,560
Weighted average number of shares for Basic:
Common stock (in shares)	3,590	3,590	3,621
Income per share for Basic:
Common stock (in dollars per share)	$ 6.49	$ 4.62	$ 4.57