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. 30, 2019	Nov. 24, 2018
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 48,242	$ 38,320
As reported - Basic (in shares)	18,951	19,142
As reported – Diluted	$ 48,242	$ 38,320
As reported - Diluted (in shares)	19,123	19,302
As reported - Diluted (in dollars per share)	$ 2.52	$ 1.99
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 40,526	$ 32,137
As reported - Basic (in shares)	15,308	15,432
As reported - Basic (in dollars per share)	$ 2.65	$ 2.08
Add: effect of dilutive potential common shares	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	172	160
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 7,716	$ 6,183
As reported - Basic (in shares)	3,643	3,710
As reported - Basic (in dollars per share)	$ 2.12	$ 1.67