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. 29, 2025	Nov. 30, 2024
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income	$ 34,363	$ 43,105
Allocation of net income for Basic:
Common stock	$ 34,363	$ 43,105
Weighted average number of shares for Basic:
Common stock (in shares)	18,148	18,586
Common Stock
Allocation of net income for Basic:
Common stock	$ 28,760	$ 36,213
Weighted average number of shares for Basic:
Common stock (in shares)	14,597	15,012
Income per share for Basic:
Common stock (in dollars per share)	$ 1.97	$ 2.41
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 5,603	$ 6,892
Weighted average number of shares for Basic:
Common stock (in shares)	3,551	3,574
Income per share for Basic:
Common stock (in dollars per share)	$ 1.58	$ 1.93