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 25, 2024	May 27, 2023	May 25, 2024	May 27, 2023
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 38,057	$ 24,276	$ 100,839	$ 76,043
As reported - Basic (in shares)	18,652	18,677	18,684	18,674
As reported - Diluted	$ 38,057	$ 24,276	$ 100,839	$ 76,043
As reported - Diluted (in shares)	18,705	18,748	18,738	18,751
As reported - Diluted (in dollars per share)	$ 2.03	$ 1.29	$ 5.38	$ 4.06
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 31,962	$ 20,394	$ 84,716	$ 63,882
As reported - Basic (in shares)	15,062	15,087	15,094	15,084
As reported - Basic (in dollars per share)	$ 2.12	$ 1.35	$ 5.61	$ 4.23
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	53	71	54	77
As reported - Diluted (in dollars per share)	$ 2.03	$ 1.29	$ 5.38	$ 4.06
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 6,095	$ 3,882	$ 16,123	$ 12,161
As reported - Basic (in shares)	3,590	3,590	3,590	3,590
As reported - Basic (in dollars per share)	$ 1.7	$ 1.08	$ 4.49	$ 3.39