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. 26, 2022	Nov. 27, 2021
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 33,957	$ 33,705
Allocation of net income for Basic:
Common Stock	$ 33,957	$ 33,705
Weighted average number of shares for Basic:
Common stock (in shares)	18,672	18,872
Common Stock
Allocation of net income for Basic:
Common Stock	$ 28,525	$ 28,291
Weighted average number of shares for Basic:
Common stock (in shares)	15,082	15,229
Income per share for Basic:
Common stock (in dollars per share)	$ 1.89	$ 1.86
Class B Common Stock
Allocation of net income for Basic:
Common Stock	$ 5,432	$ 5,414
Weighted average number of shares for Basic:
Common stock (in shares)	3,590	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 1.51	$ 1.49