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. 28, 2020	Nov. 30, 2019
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 41,896	$ 48,242
As reported - Basic (in shares)	18,890	18,951
As reported – Diluted	$ 41,896	$ 48,242
As reported - Diluted (in shares)	19,019	19,123
As reported - Diluted (in dollars per share)	$ 2.20	$ 2.52
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 35,171	$ 40,526
As reported - Basic (in shares)	15,247	15,308
As reported - Basic (in dollars per share)	$ 2.31	$ 2.65
Add: effect of dilutive potential common shares	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	129	172
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 6,725	$ 7,716
As reported - Basic (in shares)	3,643	3,643
As reported - Basic (in dollars per share)	$ 1.85	$ 2.12