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 27, 2023	May 28, 2022	May 27, 2023	May 28, 2022
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 24,276	$ 25,067	$ 76,043	$ 77,223
As reported - Basic (in shares)	18,677	18,802	18,674	18,843
As reported - Diluted	$ 24,276	$ 25,067	$ 76,043	$ 77,223
As reported - Diluted (in shares)	18,748	18,875	18,751	18,958
As reported - Diluted (in dollars per share)	$ 1.29	$ 1.33	$ 4.06	$ 4.07
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 20,394	$ 21,037	$ 63,882	$ 64,835
As reported - Basic (in shares)	15,087	15,170	15,084	15,211
As reported - Basic (in dollars per share)	$ 1.35	$ 1.39	$ 4.23	$ 4.26
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	71	73	77	115
As reported - Diluted	$ 24,276	$ 25,067	$ 76,043	$ 77,223
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 3,882	$ 4,030	$ 12,161	$ 12,388
As reported - Basic (in shares)	3,590	3,632	3,590	3,632
As reported - Basic (in dollars per share)	$ 1.08	$ 1.11	$ 3.39	$ 3.41