Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended
	Nov. 27, 2021	Nov. 28, 2020
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 33,705	$ 41,896
As reported - Basic (in shares)	18,872	18,890
As reported – Diluted	$ 33,705	$ 41,896
As reported - Diluted (in shares)	19,026	19,019
As reported - Diluted (in dollars per share)	$ 1.77	$ 2.20
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 28,291	$ 35,171
As reported - Basic (in shares)	15,229	15,247
As reported - Basic (in dollars per share)	$ 1.86	$ 2.31
Add: effect of dilutive potential common shares	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	154	129
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 5,414	$ 6,725
As reported - Basic (in shares)	3,643	3,643
As reported - Basic (in dollars per share)	$ 1.49	$ 1.85