Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 27, 2021	Feb. 29, 2020	Feb. 27, 2021	Feb. 29, 2020
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 32,585	$ 34,680	$ 74,481	$ 82,922
As reported - Basic (in shares)	18,866	18,936	18,878	18,943
As reported – Diluted	$ 32,585	$ 34,680	$ 74,481	$ 82,922
As reported - Diluted (in shares)	19,037	19,105	19,032	19,114
As reported - Diluted (in dollars per share)	$ 1.71	$ 1.82	$ 3.91	$ 4.34
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 27,349	$ 29,129	$ 62,520	$ 69,654
As reported - Basic (in shares)	15,223	15,293	15,235	15,300
As reported - Basic (in dollars per share)	$ 1.80	$ 1.90	$ 4.10	$ 4.55
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	171	169	154	171
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 5,236	$ 5,551	$ 11,961	$ 13,268
As reported - Basic (in shares)	3,643	3,643	3,643	3,643
As reported - Basic (in dollars per share)	$ 1.44	$ 1.52	$ 3.28	$ 3.64