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. 24, 2018	Nov. 25, 2017
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 38,320	$ 34,206
As reported - Basic (in shares)	19,142	20,278
As reported – Diluted	$ 38,320	$ 34,206
As reported - Diluted (in shares)	19,302	20,434
As reported - Diluted (in dollars per share)	$ 1.99	$ 1.67
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 32,137	$ 27,384
As reported - Basic (in shares)	15,432	15,462
As reported - Basic (in dollars per share)	$ 2.08	$ 1.77
Add: effect of dilutive potential common shares	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	160	156
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 6,183	$ 6,822
As reported - Basic (in shares)	3,710	4,816
As reported - Basic (in dollars per share)	$ 1.67	$ 1.42
Add: effect of dilutive potential common shares	$ 6,183	$ 6,822
Add: effect of dilutive potential common shares (in shares)	3,710	4,816