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. 26, 2022	Feb. 27, 2021	Feb. 26, 2022	Feb. 27, 2021
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 18,451	$ 32,585	$ 52,156	$ 74,481
As reported - Basic (in shares)	18,845	18,866	18,860	18,878
As reported – Diluted	$ 18,451	$ 32,585	$ 52,156	$ 74,481
As reported - Diluted (in shares)	18,967	19,037	18,999	19,032
As reported - Diluted (in dollars per share)	$ 0.97	$ 1.71	$ 2.75	$ 3.91
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 15,492	$ 27,349	$ 43,792	$ 62,520
As reported - Basic (in shares)	15,210	15,223	15,225	15,235
As reported - Basic (in dollars per share)	$ 1.02	$ 1.80	$ 2.88	$ 4.10
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	122	171	139	154
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 2,959	$ 5,236	$ 8,364	$ 11,961
As reported - Basic (in shares)	3,635	3,643	3,635	3,643
As reported - Basic (in dollars per share)	$ 0.81	$ 1.44	$ 2.30	$ 3.28