Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended
	Nov. 30, 2024	Nov. 25, 2023
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 43,105	$ 42,325
Allocation of net income for Basic:
Common stock	$ 43,105	$ 42,325
Weighted average number of shares for Basic:
Common stock (in shares)	18,586	18,702
Common Stock
Allocation of net income for Basic:
Common stock	$ 36,213	$ 35,566
Weighted average number of shares for Basic:
Common stock (in shares)	15,012	15,111
Income per share for Basic:
Common stock (in dollars per share)	$ 2.41	$ 2.35
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 6,892	$ 6,759
Weighted average number of shares for Basic:
Common stock (in shares)	3,574	3,590
Income per share for Basic:
Common stock (in dollars per share)	$ 1.93	$ 1.88