Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	May 28, 2022	May 29, 2021	May 28, 2022	May 29, 2021
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 25,067	$ 42,016	$ 77,223	$ 116,497
As reported - Basic (in shares)	18,802	18,881	18,843	18,881
As reported – Diluted	$ 25,067	$ 42,016	$ 77,223	$ 116,497
As reported - Diluted (in shares)	18,875	19,051	18,958	19,041
As reported - Diluted (in dollars per share)	$ 1.33	$ 2.21	$ 4.07	$ 6.12
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 21,037	$ 35,270	$ 64,835	$ 97,792
As reported - Basic (in shares)	15,170	15,238	15,211	15,238
As reported - Basic (in dollars per share)	$ 1.39	$ 2.31	$ 4.26	$ 6.42
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	73	170	115	160
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 4,030	$ 6,746	$ 12,388	$ 18,705
As reported - Basic (in shares)	3,632	3,643	3,632	3,643
As reported - Basic (in dollars per share)	$ 1.11	$ 1.85	$ 3.41	$ 5.13