Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended				6 Months Ended
	Mar. 01, 2025	Nov. 30, 2024	Feb. 24, 2024	Nov. 25, 2023	Mar. 01, 2025	Feb. 24, 2024
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 24,459	$ 43,105	$ 20,457	$ 42,325	$ 67,564	$ 62,782
Allocation of net income for Basic:
Common stock	$ 24,459		$ 20,457		$ 67,564	$ 62,782
Weighted average number of shares for Basic:
Common stock (in shares)	18,567		18,696		18,577	18,700
Common Stock
Allocation of net income for Basic:
Common stock	$ 20,559		$ 17,188		$ 56,778	$ 52,754
Weighted average number of shares for Basic:
Common stock (in shares)	15,009		15,106		15,011	15,110
Income per share for Basic:
Common stock (in dollars per share)	$ 1.37		$ 1.14		$ 3.78	$ 3.49
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 3,900		$ 3,269		$ 10,786	$ 10,028
Weighted average number of shares for Basic:
Common stock (in shares)	3,558		3,590		3,566	3,590
Income per share for Basic:
Common stock (in dollars per share)	$ 1.1		$ 0.91		$ 3.02	$ 2.79